Weak Galerkin finite element method for second order problems on curvilinear polytopal meshes with Lipschitz continuous edges or faces

Abstract

In this paper, the weak Galerkin finite element method for second order problems on curvilinear polytopal meshes with Lipschitz continuous edges or faces was analyzed. The method here is designed to deal with second order problems with complex boundary conditions or complex interfaces. With Lipschitz continuous boundary or interface, the method's optimal convergence rate for $H^1$ and $L^2$ error estimates were obtained. Arbitrary high orders can be achieved.Comment: arXiv admin note: substantial text overlap with arXiv:1805.0092