Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Applied Mathematics (49)
- Analysis (17)
- Discrete Mathematics and Combinatorics (13)
- Dynamical Systems (9)
- Statistics and Probability (8)
-
- Geometry and Topology (7)
- Engineering (5)
- Algebra (4)
- Life Sciences (4)
- Physics (4)
- Control Theory (3)
- Algebraic Geometry (2)
- Computational Engineering (2)
- Education (2)
- Medicine and Health Sciences (2)
- Ordinary Differential Equations and Applied Dynamics (2)
- Science and Mathematics Education (2)
- Analytical, Diagnostic and Therapeutic Techniques and Equipment (1)
- Cell and Developmental Biology (1)
- Civil and Environmental Engineering (1)
- Computer Engineering (1)
- Computer Sciences (1)
- Earth Sciences (1)
- Electrical and Computer Engineering (1)
- Forest Management (1)
- Forest Sciences (1)
- Harmonic Analysis and Representation (1)
- Horticulture (1)
- Keyword
-
- Finite element method (23)
- Numerical analysis (18)
- Galerkin methods (17)
- Polynomials (11)
- Stochastic analysis (11)
-
- Mathematical statistics (10)
- Boundary value problems (9)
- Algorithms (8)
- Random variables -- Mathematical models (8)
- Approximation theory (7)
- Mathematical optimization (6)
- Convex functions (5)
- Discontinuous functions (5)
- Eigenvalues (5)
- Thermodynamics (5)
- Biomimicry (4)
- Differential equations (4)
- Elasticity (4)
- Error analysis (Mathematics) (4)
- Mathematical physics (4)
- Maxwell equations (4)
- Multigrid methods (Numerical analysis) (4)
- Optical coatings -- Design and construction (4)
- Stochastic orders (4)
- Chaotic behavior in systems (3)
- Combinatorial analysis (3)
- Commutative algebra (3)
- Elliptic functions (3)
- Helmholtz equation (3)
- Lagrange equations (3)
Articles 121 - 150 of 171
Full-Text Articles in Mathematics
Biomimetic Subwavelength Antireflective Gratings On Gaas, Chih-Hung Sun, Brian J. Ho, Bin Jiang, Peng Jiang
Biomimetic Subwavelength Antireflective Gratings On Gaas, Chih-Hung Sun, Brian J. Ho, Bin Jiang, Peng Jiang
Mathematics and Statistics Faculty Publications and Presentations
We have developed a simple and scalable bottom-up approach for fabricating moth-eye antireflective coatings on GaAs substrates. Monolayer, non-close-packed silica colloidal crystals are created on crystalline GaAs wafers by a spin-coating-based single-layer reduction technique. These colloidal monolayers can be used as etching masks during a BCl_3 dry-etch process to generate subwavelength-structured antireflective gratings directly on GaAs substrates. The gratings exhibit excellent broadband antireflective properties, and the specular reflection matches with the theoretical prediction using a rigorous coupled-wave analysis model. These bioinspired antireflection coatings have important technological applications ranging from efficient solar cells to IR detectors
How Students Use Mathematical Resources In An Electrostatics Context, Dawn C. Meredith, Karen A. Marrongelle
How Students Use Mathematical Resources In An Electrostatics Context, Dawn C. Meredith, Karen A. Marrongelle
Mathematics and Statistics Faculty Publications and Presentations
We present evidence that although students’ mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin’s symbolic forms. We find that students use notions of “dependence” and “parts-of-a-whole” to successfully guide their work, even in novel situations. We also present evidence that students’ naive conceptions of the limit may prevent them from viewing integrals as sums.
Bioinspired Broadband Antireflection Coatings On Gasb, Wei-Lun Min, Amaury P. Betancourt, Peng Jiang, Bin Jiang
Bioinspired Broadband Antireflection Coatings On Gasb, Wei-Lun Min, Amaury P. Betancourt, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report an inexpensive yet scalable templating technique for fabricating moth-eye antireflection gratings on gallium antimonide substrates. Non-close-packed colloidal monolayers are utilized as etching masks to pattern subwavelength-structured nipple arrays on GaSb. The resulting gratings exhibit superior broadband antireflection properties and thermal stability than conventional multilayer dielectric coatings. The specular reflection of the templated nipple arrays match with the theoretical predictions using a rigorous coupled-wave analysis model. The effect of the nipple shape and size on the antireflection properties has also been investigated by the same model. These biomimetic coatings are of great technological importance in developing efficient thermophotovoltaic cells.
Broadband Moth-Eye Antireflection Coatings On Silicon, Chih-Hung Sun, Peng Jiang, Bin Jiang
Broadband Moth-Eye Antireflection Coatings On Silicon, Chih-Hung Sun, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report a bioinspired templating technique for fabricating broadband antireflection coatings that mimic antireflective moth eyes. Wafer-scale, subwavelength-structured nipple arrays are directly patterned on silicon using spin-coated silica colloidal monolayers as etching masks. The templated gratings exhibit excellent broadband antireflection properties and the normal-incidence specular reflection matches with the theoretical prediction using a rigorous coupled-wave analysis (RCWA) model. We further demonstrate that two common simulation methods, RCWA and thin-film multilayer models, generate almost identical prediction for the templated nipple arrays. This simple bottom-up technique is compatible with standard microfabrication, promising for reducing the manufacturing cost of crystalline silicon solar cells.
Templated Biomimetic Multifunctional Coatings, Chih-Hung Sun, Adriel Gonzalez, Nicholas C. Linn, Peng Jiang, Bin Jiang
Templated Biomimetic Multifunctional Coatings, Chih-Hung Sun, Adriel Gonzalez, Nicholas C. Linn, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report a bioinspired templating technique for fabricating multifunctional optical coatings that mimic both unique functionalities of antireflective moth eyes and superhydrophobic cicada wings. Subwavelength-structured fluoropolymer nipple arrays are created by a soft-lithography-like process. The utilization of fluoropolymers simultaneously enhances the antireflective performance and the hydrophobicity of the replicated films. The specular reflectivity matches the optical simulation using a thin-film multilayer model. The dependence of the size and the crystalline ordering of the replicated nipples on the resulting antireflective properties have also been investigated by experiment and modeling. These biomimetic materials may find important technological application in self-cleaning antireflection coatings.
Multisymplectic Theory Of Balance Systems, I, Serge Preston
Multisymplectic Theory Of Balance Systems, I, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this paper we are presenting the theory of balance equations of the Continuum Thermodynamics (balance systems) in a geometrical form using Poincare-Cartan formalism of the Multisymplectic Field Theory. A constitutive relation C of a balance system BC is realized as a mapping between a (partial) 1-jet bundle of the configurational bundle π : Y ͢ X and the extended dual bundle similar to the Legendre mapping of the Lagrangian Field Theory. Invariant (variational) form of the balance system BC is presented in three different forms and the space of admissible variations is defined and studied. Action of automorphisms …
Order Restricted Inference For Comparing The Cumulative Incidence Of A Competing Risk Over Several Populations, Hammou El Barmi, Subhash C. Kochar, Hari Mukerjee
Order Restricted Inference For Comparing The Cumulative Incidence Of A Competing Risk Over Several Populations, Hammou El Barmi, Subhash C. Kochar, Hari Mukerjee
Mathematics and Statistics Faculty Publications and Presentations
There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this paper we propose an asymptotically distribution-free test when the alternative is that the incidence functions are linearly ordered, but not equal. The motivation stems from the fact that in many examples such a linear ordering seems reasonable intuitively and is borne out generally from empirical observations. These tests are more powerful when the ordering is justified. We also provide estimators of the incidence functions under …
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
Mathematics and Statistics Faculty Publications and Presentations
We study an indefinite metric G which was introduced by R. Mrugala and is defined on the contact phase space (P, θ) of a homogeneous thermodynamical system. We describe the curvature properties and the isometry group of the metric G. We established an isomorphism of the space (P, θ, G) with the Heisenberg Lie group Hn, endowed with the right invariant contact structure and the right invariant indefinite metric. The lift of the metric G to the symplectization of contact space (P, θ) and its properties are studied. Finally we introduce the "hyperbolic projectivization" of the space …
Utilization Of Revoicing Based On Learners‘ Thinking In An Inquiry-Oriented Differential Equations Class, Oh Kwon Nam, Mi Kyung Ju, Chris Rasmussen, Karen A. Marrongelle, Jae Hee Park, Kyoung Hee Cho, Jung Sook Park, Jee Hyun Park
Utilization Of Revoicing Based On Learners‘ Thinking In An Inquiry-Oriented Differential Equations Class, Oh Kwon Nam, Mi Kyung Ju, Chris Rasmussen, Karen A. Marrongelle, Jae Hee Park, Kyoung Hee Cho, Jung Sook Park, Jee Hyun Park
Mathematics and Statistics Faculty Publications and Presentations
Researchers of mathematics education are increasingly interested in a teacher's discursive moves, which refer to deliberate actions taken by a teacher to participate in or influence debate and discussion in the mathematics classroom. This study explored one teacher's discursive moves in an undergraduate inquiry-oriented mathematics class. The data for this study come from four class sessions in which students investigated initial value problems as represented by the phase portrait of a system of differential equations. Through the analysis and a review of the literature, we identified four categories of a teacher's discursive moves: revoicing, questioning/requesting, telling, and managing. This report …
Correction To "Stochastic Comparisons Of Parallel Systems When Components Have Proportional Hazard Rates", Subhash C. Kochar, Maochao Xu
Correction To "Stochastic Comparisons Of Parallel Systems When Components Have Proportional Hazard Rates", Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In the article "Stochastic comparisons of parallel systems when component have proportional hazard rates" we found a gap in the middle of the proof of Theorem 3.2. Therefore, we do not know whether Theorem 3.2 is true for the reverse hazard rate order. However, we could prove the following weaker result for the stochastic order.
Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Mathematics and Statistics Faculty Publications and Presentations
In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to introducing our new technique for constructing the extensions, and its application to the case of polynomial extensions from H½(∂K) into H¹(K), for any tetrahedron K.
Asymptotic And Numerical Techniques For Resonances Of Thin Photonic Structures, Jay Gopalakrishnan, Shari Moskow, Fadil Santosa
Asymptotic And Numerical Techniques For Resonances Of Thin Photonic Structures, Jay Gopalakrishnan, Shari Moskow, Fadil Santosa
Mathematics and Statistics Faculty Publications and Presentations
We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiting resonance problem as the thickness goes to zero, and for the case of a simple resonance, find a first order correction. The limiting problem and the correction are in one less space dimension, which can make the approach …
A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak
A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.
Uniform Materials And The Multiplicative Decomposition Of The Deformation Gradient In Finite Elasto-Plasticity, Vincenzo Ciancio, Marina Dolfin, Mauro Francaviglia, Serge Preston
Uniform Materials And The Multiplicative Decomposition Of The Deformation Gradient In Finite Elasto-Plasticity, Vincenzo Ciancio, Marina Dolfin, Mauro Francaviglia, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we analyze the relation between the multiplicative decomposition F = F e F p of the deformation gradient as a product of the elastic and plastic factors and the theory of uniform materials. We prove that postulating such a decomposition is equivalent to having a uniform material model with two configurations – total φ and the inelastic φ1. We introduce strain tensors characterizing different types of evolutions of the material and discuss the form of the internal energy and that of the dissipative potential. The evolution equations are obtained for the configurations (φ, φ1) and the material …
Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak
Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
The finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither Hermitian nor definite when the coefficient function is complex valued. For such problems, under a uniqueness assumption, we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero. Then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number, providing an efficient solver for computing discrete approximations. Numerical experiments, while confirming the theory, …
Templated Fabrication Of Large Area Subwavelength Antireflection Gratings On Silicon, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang
Templated Fabrication Of Large Area Subwavelength Antireflection Gratings On Silicon, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report a cheap and scalable bottom-up technique for fabricating wafer-scale, subwavelength-structured antireflection coatings on single-crystalline silicon substrates. Spin-coated monolayer colloidal crystals are utilized as shadow masks to generate metallic nanohole arrays. Inverted pyramid arrays in silicon can then be templated against nanoholes by anisotropic wet etching. The resulting subwavelength gratings greatly suppress specular reflection at normal incidence. The reflection spectra for flat silicon and the templated gratings at long wavelengths agree well with the simulated results using a rigorous coupled wave analysis model. These subwavelength gratings are of great technological importance in crystalline silicon solar cells.
Self-Assembled Biomimetic Antireflection Coatings, Nicholas C. Linn, Chih-Hung Sun, Peng Jiang, Bin Jiang
Self-Assembled Biomimetic Antireflection Coatings, Nicholas C. Linn, Chih-Hung Sun, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
The authors report a simple self-assembly technique for fabricating antireflection coatings that mimic antireflective moth eyes. Wafer-scale, nonclose-packed colloidal crystals with remarkable large hexagonal domains are created by a spin-coating technology. The resulting polymer-embedded colloidal crystals exhibit highly ordered surface modulation and can be used directly as templates to cast poly(dimethylsiloxane) (PDMS) molds. Moth-eye antireflection coatings with adjustable reflectivity can then be molded against the PDMS master. The specular reflection of replicated nipple arrays matches the theoretical prediction using a thin-film multilayer model. These biomimetic films may find important technological application in optical coatings and solar cells.
Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu
Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
Let Χ1, … Χn be independent random variables with Χᵢ having survival function Fλᵢ, i=1, … , n, and let Y₁, … , Yn be a random sample with common population survival distribution Fλ, where λ = Σᵢ=₁nλᵢl n. Let Χn:n and Yn:n denote the lifetimes of the parallel systems consisting of these components, respectively. It is shown that Xn:n is greater than Yn:n in terms of likelihood ratio order. It is also proved that the sample range Χn:n - Χ₁:n is larger than Yn n:n - Y₁:n according to reverse hazard rate ordering. These two results …
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
This paper reviews some recent results on stochastic orders and dependence among order statistics when the observations are independent and follow the proportional hazard rates model.
Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang
Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang
Mathematics and Statistics Faculty Publications and Presentations
The standard continuous Galerkin (CG) finite element method for second order elliptic problems suffers from its inability to provide conservative flux approximations, a much needed quantity in many applications. We show how to overcome this shortcoming by using a two step postprocessing. The first step is the computation of a numerical flux trace defined on element inter- faces and is motivated by the structure of the numerical traces of discontinuous Galerkin methods. This computation is non-local in that it requires the solution of a symmetric positive definite system, but the system is well conditioned independently of mesh size, so it …
The Topology Of Surface Mediatrices, James Bernhard, J. J. P. Veerman
The Topology Of Surface Mediatrices, James Bernhard, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Given a pair of distinct points p and q in a metric space with distance d, the mediatrix is the set of points x such that d(x,p)=d(x,q). In this paper, we examine the topological structure of mediatrices in connected, compact, closed 2-manifolds whose distance function is inherited from a Riemannian metric. We determine that such mediatrices are, up to homeomorphism, finite, closed simplicial 1-complexes with an even number of incipient edges emanating from each vertex. Using this and results from [J.J.P. Veerman, J. Bernhard, Minimally separating sets, mediatrices and Brillouin spaces, Topology Appl., in press], we give the classification …
Correction To "Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering", Baha-Eldin Khaledi, Subhash C. Kochar
Correction To "Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering", Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
In the article published last year, three inequalities should be in the opposite direction.
The Convergence Of V-Cycle Multigrid Algorithms For Axisymmetric Laplace And Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak
The Convergence Of V-Cycle Multigrid Algorithms For Axisymmetric Laplace And Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
We investigate some simple finite element discretizations for the axisymmetric Laplace equation and the azimuthal component of the axisymmetric Maxwell equations as well as multigrid algorithms for these discretizations. Our analysis is targeted at simple model problems and our main result is that the standard V-cycle with point smoothing converges at a rate independent of the number of unknowns. This is contrary to suggestions in the existing literature that line relaxations and semicoarsening are needed in multigrid algorithms to overcome difficulties caused by the singularities in the axisymmetric Maxwell problems. Our multigrid analysis proceeds by applying the well known regularity …
Kernels Of Directed Graph Laplacians, John S. Caughman Iv, J. J. P. Veerman
Kernels Of Directed Graph Laplacians, John S. Caughman Iv, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Let G denote a directed graph with adjacency matrix Q and in- degree matrix D. We consider the Kirchhoff matrix L = D − Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals the number of connected components of G. This fact has a meaningful generalization to directed graphs, as was observed by Chebotarev and Agaev in 2005. Since this result has many important applications in the sciences, we offer an independent and self-contained proof of their theorem, showing in this paper …
Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar
Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of …
Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan
Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new …
The Terwilliger Algebra Of An Almost-Bipartite P- And Q-Polynomial Association Scheme, John S. Caughman Iv, Mark S. Maclean, Paul M. Terwilliger
The Terwilliger Algebra Of An Almost-Bipartite P- And Q-Polynomial Association Scheme, John S. Caughman Iv, Mark S. Maclean, Paul M. Terwilliger
Mathematics and Statistics Faculty Publications and Presentations
Let Y denote a D-class symmetric association scheme with D≥3, and suppose Y is almost-bipartite P- and Q-polynomial. Let x denote a vertex of Y and let T=T(x) denote the corresponding Terwilliger algebra. We prove that any irreducible T-module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the isomorphism class of W as a T-module is determined by two parameters, the dual endpoint and diameter of W. We find a recurrence which gives the multiplicities with which the …
Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Incompressible Finite Elements Via Hybridization. Part Ii: The Stokes System In Three Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We introduce a method that gives exactly incompressible velocity approximations to Stokes ow in three space dimensions. The method is designed by extending the ideas in Part I (http://archives.pdx.edu/ds/psu/10914) of this series, where the Stokes system in two space dimensions was considered. Thus we hybridize a vorticity-velocity formulation to obtain a new mixed method coupling approximations of tangential velocity and pressure on mesh faces. Once this relatively small tangential velocity-pressure system is solved, it is possible to recover a globally divergence-free numerical approximation of the fluid velocity, an approximation of the vorticity whose tangential component is continuous across …
Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we introduce a new and efficient way to compute exactly divergence-free velocity approximations for the Stokes equations in two space dimensions. We begin by considering a mixed method that provides an exactly divergence-free approximation of the velocity and a continuous approximation of the vorticity. We then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique. This novel formulation bypasses the difficult task of constructing an exactly divergence-free basis for velocity approximations. Moreover, the discrete system resulting from our method has fewer degrees …
Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz
Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz
Mathematics and Statistics Faculty Publications and Presentations
In this note, we provide a conveniently implementable basis for simplicial Nédélec spaces of any order in any space dimension. The main feature of the basis is that it is expressed solely in terms of the barycentric coordinates of the simplex.