Anisotropic Quasi-Wilson Element with Conforming Finite Element Approximation for Coupled Continuum Pipe-Flow/Darcy Model in Karst Aquifers

Abstract

This paper presents a numerical method for solving systems of partial differential equations describing flow in porous media with an embedded and inclined conduit pipe. This work considers a coupled continuum pipe-flow/Darcy model. The numerical schemes presented are based on combinations of the quasi-Wilson element on anisotropic mesh and the conforming finite element on regular mesh. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in both L² and H¹ norms are obtained independent of the regularity condition on the mesh. Numerical examples show the accuracy and efficiency of the proposed scheme.