Optimal error bound for immersed weak Galerkin finite element method for elliptic interface problems

Abstract

In Mu and Zhang (2019), an immersed weak Galerkin finite element method (IWG-FEM) is developed for solving elliptic interface problems and it is proved that this method has optimal a-priori error estimate in an energy norm under artificial smoothness assumption on the solution. In this study, we prove that IWG-FEM converges optimally in energy norm under natural smoothness assumption on solution. Furthermore, we show that IWG-FEM converges optimally in the L2 norm which did not present in Mu and Zhang (2019) because of the artificial H3 smoothness requirement. A series of numerical experiments are conducted and reported to verify the theoretical finding.