A Convergence Result of a Linear SUSHI Scheme Using Characteristics Method for a Semi-linear Parabolic Equation

摘要

This work is an extension and improvement of [1] which dealt with a convergence analysis of a FVS (Finite Volume Scheme) using the Characteristic method for non-stationary LINEAR advection-diffusion equations. In this note, we address the case of non-stationary SEMILINEAR advection-diffusion equations. We establish two FVSs, one is linear and the other is nonlinear, which uses the discrete gradient developed in [5] and an approximation of the equation using the Characteristic method. For the sake of simplicity of the present note, we only focus on the linear scheme and we prove its convergence. The convergence analysis relies mainly on a well developed new discrete a prior estimate. This work is a continuation of the previous one [2] in which we derived directly a finite volume scheme for the semilinear heat equation along with a convergence analysis.