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Full-Text Articles in Physical Sciences and Mathematics
Symmetric Nonconforming Mixed Finite Elements For Linear Elasticity, Jay Gopalakrishnan, Johnny Guzmán
Symmetric Nonconforming Mixed Finite Elements For Linear Elasticity, Jay Gopalakrishnan, Johnny Guzmán
Mathematics and Statistics Faculty Publications and Presentations
We present a family of mixed methods for linear elasticity that yield exactly symmetric, but only weakly conforming, stress approximations. The method is presented in both two and three dimensions (on triangular and tetrahedral meshes). The method is efficiently implementable by hybridization. The degrees of freedom of the Lagrange multipliers, which approximate the displacements at the faces, solve a symmetric positive-definite system. The design and analysis of this method is motivated by a new set of unisolvent degrees of freedom for symmetric polynomial matrices. These new degrees of freedom are also used to give a new simple calculation of the …
Commuting Smoothed Projectors In Weighted Norms With An Application To Axisymmetric Maxwell Equations, Jay Gopalakrishnan, Minah Oh
Commuting Smoothed Projectors In Weighted Norms With An Application To Axisymmetric Maxwell Equations, Jay Gopalakrishnan, Minah Oh
Mathematics and Statistics Faculty Publications and Presentations
We construct finite element projectors that can be applied to functions with low regularity. These projectors are continuous in a weighted norm arising naturally when modeling devices with axial symmetry. They have important commuting diagram properties needed for finite element analysis. As an application, we use the projectors to prove quasioptimal convergence for the edge finite element approximation of the axisymmetric time-harmonic Maxwell equations on nonsmooth domains. Supplementary numerical investigations on convergence deterioration at high wavenumbers and near Maxwell eigenvalues and are also reported.
A Second Elasticity Element Using The Matrix Bubble, Jay Gopalakrishnan, Johnny Guzmán
A Second Elasticity Element Using The Matrix Bubble, Jay Gopalakrishnan, Johnny Guzmán
Mathematics and Statistics Faculty Publications and Presentations
We presented a family of finite elements that use a polynomial space augmented by certain matrix bubbles in Cockburn et al. (2010) A new elasticity element made for enforcing weak stress symmetry. Math. Comput., 79, 1331–1349 . In this sequel we exhibit a second family of elements that use the same matrix bubble. This second element uses a stress space smaller than the first while maintaining the same space for rotations (which are the Lagrange multipliers corresponding to a weak symmetry constraint). The space of displacements is of one degree less than the first method. The analysis, while similar to …