Weak Galerkin coupled with conforming finite element method for hybrid-dimensional fracture model

Abstract

In this paper, we propose the weak Galerkin coupled with conforming finite element method to solve the hybrid-dimensional fracture problem, which couples n-dimensional Darcy flow in the porous matrix with (n−1)-dimensional flow in the fracture. The generalized Robin type interface conditions present in the coupling scheme. We derive the optimal error estimates for L2 and energy norms with arbitrary degree polynomials. The error rate obtained by numerical examples agrees with the analysis results on both polygonal mesh and nonmatching mesh. Results of numerical examples also show that the proposed scheme is robust to the parameters in the reduced fracture model.