Convergence Analysis of a Finite Volume Gradient Scheme for a Linear Parabolic Equation Using Characteristic Methods

Abstract

The first aim of this work is to establish a finite volume scheme using the Characteristic method for non-stationary advection-diffusion equations. The second aim is to analyze the convergence order of this scheme. The finite volume method considered here has been developed recently in [3] to approximate heterogeneous and anisotropic diffusion problems using a general class of nonconforming meshes. The formulation of schemes using the finite volume method of [3] can be obtained by replacing the gradient of the exact solution by a stable and consistent discrete gradient. This work is a continuation of the previous ones [1, 2] in which we derived directly a finite volume scheme for the heat equation along with a convergence analysis.