Discontinuous Galerkin Immersed Finite Volume Element Method for Anisotropic Flow Models in Porous Medium

Abstract

By choosing the trial function space to the immersed finite element space and the test function space to be piecewise constant function space, we develop a discontinuous Galerkin immersed finite volume element method to solve numerically a kind of anisotropic diffusion models governed by the elliptic interface problems with discontinuous tensor-conductivity. The existence and uniqueness of the discrete scheme are proved, and an optimal-order energy-norm estimate and $L^2$-norm estimate for the numerical solution are derived.