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Research Article | Open Access

Simplified weak Galerkin finite element methods for biharmonic equations on non-convex polytopal meshes

Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
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Abstract

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.

Keywords

weak Galerkinweak second order partial derivativestabilizer-freebubble functionsnon-convex, polytopal meshesbiharmonic equations

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Electronic Research Archive
Volume 33 Issue 3,
March 2025
Pages 1523-1540
DOI: 10.3934/era.2025072

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Cite this article:
Wang C. Simplified weak Galerkin finite element methods for biharmonic equations on non-convex polytopal meshes. Electronic Research Archive, 2025, 33(3): 1523-1540. https://doi.org/10.3934/era.2025072

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Received: 17 December 2024
Revised: 23 February 2025
Accepted: 03 March 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)