A Modified Primal-Dual Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence Form
Year: 2021
Author: Chunmei Wang
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 500–523
Abstract
A modified primal-dual weak Galerkin (M-PDWG) finite element method is designed for the second order elliptic equation in non-divergence form. Compared with the existing PDWG methods proposed in [6], the system of equations resulting from the M-PDWG scheme could be equivalently simplified into one equation involving only the primal variable by eliminating the dual variable (Lagrange multiplier). The resulting simplified system thus has significantly fewer degrees of freedom than the one resulting from existing PDWG scheme. Optimal order error estimates are derived for the numerical approximations in the discrete $H^2$-norm, $H^1$-norm and $L^2$-norm respectively. Extensive numerical results are demonstrated for both the smooth and non-smooth coefficients on convex and non-convex domains to verify the accuracy of the theory developed in this paper.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-19112
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 500–523
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Primal-dual weak Galerkin finite element methods non-divergence form Cordès condition polyhedral meshes.