Weak Galerkin finite element method for Poisson's equation on polytopal meshes with arbitrary small edges or faces
arXiv:1805.00921h-index: 10
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Provides theoretical guarantees for a numerical method on challenging mesh geometries, benefiting computational scientists using polytopal meshes.
The paper analyzes the weak Galerkin finite element method for Poisson's equation on polytopal meshes with arbitrarily small edges or faces, proving optimal convergence orders for H1 and L2 error estimates under shape-regular assumptions.
In this paper, the weak Galerkin finite element method for second order elliptic problems employing polygonal or polyhedral meshes with arbitrary small edges or faces was analyzed. With the shape regular assumptions, optimal convergence order for $H^1$ and $L_2$ error estimates were obtained. Also element based and edge based error estimates were proved.