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A Posteriori Error Estimates For Maxwell's Equations Using Auxiliary Subspace Techniques, Ahmed El Sakori

Dissertations and Theses

The aim of our work is to construct provably efficient and reliable error estimates of discretization error for Nédélec (edge) element discretizations of Maxwell's equations on tetrahedral meshes. Our general approach for estimating the discretization error is to compute an approximate error function by solving an associated problem in an auxiliary space that is chosen so that:

-Efficiency and reliability results for the computed error estimates can be established under reasonable and verifiable assumptions.

-The linear system used to compute the approximate error function has condition number bounded independently of the discretization parameter.

In many applications, it is some functional …

Analysis On Some Basic Ion Channel Modeling Problems, Zhen Chao

Theses and Dissertations

The modeling and simulation of ion channel proteins are essential to the study of many vital physiological processes within a biological cell because most ion channel properties are very difficult to address experimentally in biochemistry. They also generate a lot of new numerical issues to be addressed in applied and computational mathematics. In this dissertation, we mainly deal with some numerical issues that are arisen from the numerical solution of one important ion channel dielectric continuum model, Poisson-Nernst-Planck (PNP) ion channel model, based on the finite element approximation approach under different boundary conditions and unstructured tetrahedral meshes. In particular, we …

Advanced Arbitrary Lagrangian-Eulerian Finite Element Methods For Unsteady Multiphysics Problems Involving Moving Interfaces/Boundaries, Rihui Lan

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation, two kinds of arbitrary Lagrangian-Eulerian (ALE)-finite element methods (FEM) within the monolithic approach are studied for unsteady multiphysics coupling problems involving the moving interfaces/boundaries. For the classical affine-type ALE mapping that is studied in the first part of this dissertation, we develop the monolithic ALE-FEM and conduct stability and optimal convergence analyses in the energy norm for the transient Stokes/parabolic interface problem with jump coefficients, and more realistically, for the dynamic fluid-structure interaction (FSI) problems by taking the discrete ALE mapping and the discrete mesh velocity into a careful consideration of our numerical analyses and computations, where …