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Curved Elements in Weak Galerkin Finite Element Methods

10/30/2022

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by Dan Li, et al.

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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 H^1-norm and the L^2-norm are established. Numerical results are reported to demonstrate the performance of the weak Galerkin methods on general curved polygonal partitions.

Dan Li
50 publications
Chunmei Wang
31 publications
JunPing Wang
26 publications

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