9 papers
Wavenumber-explicit stability and preasymptotic error analysis of UPML finite element method for obstacle scattering problems
Yuhao Wang, Weiying Zheng
This paper develops a wavenumber-explicit stability and preasymptotic error analysis for finite element approximation of the two-dimensional Helmholtz scattering problem with a uni…
hp-Optimal DG Approximation and Robust Schwarz Decompositions on One-Irregular Cubical Meshes
Situan Li, Weiying Zheng
We study hp approximation and additive Schwarz decompositions for variable-order cubical finite element spaces on one-irregular meshes. For fitted homogeneous diffusion interface p…
Stable Triangle Projections for Variable-Degree Tetrahedral Spaces and Uniform IPDG Preconditioning
Situan Li, Weiying Zheng
The main ingredient of this paper is an edge-local variable-degree projection on a triangle that is uniformly stable in both L2 and H1. We use this two-dimensional operator in two…
Weighted hp-Uniform Decompositions for H^k-Type Tensor-Product Spaces in Arbitrary Dimension
Situan Li, Weiying Zheng
We establish weighted hp-uniform vertex-patch decompositions in arbitrary space dimension d >= 1 for tensor-product discretizations of H^k-type conforming and nonconforming spaces,…
Owner-selected bubble transforms and coefficient-robust Schwarz preconditioners for variable-degree finite elements
Situan Li, Weiying Zheng
We construct - and -robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree finite element discretizations of conforming…
Trace-Preserving hp Interpolation and Polynomial Liftings on Conforming Hexahedral Meshes
Situan Li, Weiying Zheng
Trace-compatible polynomial extensions are a recurring local ingredient in high-order finite element analysis on conforming hexahedral meshes. They are needed whenever prescribed e…