Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes

Fuente: arXiv
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Main Author: Wang, Chunmei
Format: Preprint
Published: 2024
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author Wang, Chunmei
author_facet Wang, Chunmei
contents This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite element partitions, utilizing bubble functions as a critical analytical tool. The simplified WG method is symmetric and positive definite. Optimal-order error estimates are established for WG approximations in both the discrete $H^2$ norm and the $L^2$ norm.
format Preprint
id arxiv_https___arxiv_org_abs_2412_11315
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes
Wang, Chunmei
Numerical Analysis
65N30, 65N15, 65N12, 65N20
This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite element partitions, utilizing bubble functions as a critical analytical tool. The simplified WG method is symmetric and positive definite. Optimal-order error estimates are established for WG approximations in both the discrete $H^2$ norm and the $L^2$ norm.
title Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes
topic Numerical Analysis
65N30, 65N15, 65N12, 65N20
url https://arxiv.org/abs/2412.11315