Curved Elements in Weak Galerkin Finite Element Methods

2022/10/30 by Dan Li, Li, Dan, Chunmei Wang +3 · 4 citations
Engineering · #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2210.16907

openalex publication_date 2022/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on the boundary of the whole domain in two dimensions. The optimal orders of error estimates for the weak Galerkin approximations in both the H¹-norm and the L²-norm are established. Numerical results are reported to demonstrate the performance of the weak Galerkin methods on general curved polygonal partitions.

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