Finite volume discretization of a class of parabolic equations with discontinuous and oscillating coefficients

Abstract

In this paper we consider the numerical approximation of a class of parabolic equations with highly oscillating and discontinuous coefficients. We use the method of lines with a finite volumes approach to discretize this problem. This discretization leads to an ordinary differential equation (ODE). We then analyze two families of numerical schemes corresponding to explicit and implicit discretization of the obtained ODE. Numerical results comparing the approximation obtained by this method and the homogenized problem's solution are presented. They show that this method is accurate and robust for the class of problems studied.Mathematics Subject Classification: 65M08, 65M20