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arXiv:2501.02590 [math.NA]AbstractReferencesReviewsResources

Auto-Stabilized Weak Galerkin Finite Element Methods for Stokes Equations on Non-Convex Polytopal Meshes

Chunmei Wang, Shangyou Zhang

Published 2025-01-05Version 1

This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method accommodates both convex and non-convex polytopal elements in finite element partitions, leveraging bubble functions as a key analytical tool. The simplified WG method is symmetric and positive definite, and optimal-order error estimates are derived for WG approximations in both the discrete $H^1$ norm and the $L^2$ norm.

Comments: 30 pages, 8 tables, 8 figures
Categories: math.NA, cs.NA
Subjects: 65N30, 65N15, 65N12, 65N20
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