Convergence of a Finite Volume Scheme for a Corrosion Model

TL;DR

This paper proves the convergence of a combined implicit Euler and Scharfetter-Gummel finite volume scheme for modeling corrosion in nuclear waste repositories, providing a reliable numerical approach for such complex PDE systems.

Contribution

It introduces and analyzes a novel numerical scheme combining implicit Euler and Scharfetter-Gummel methods for corrosion PDE models, establishing its convergence.

Findings

Proves convergence of the proposed numerical scheme.

Provides a rigorous mathematical analysis of the scheme.

Applicable to corrosion modeling in nuclear waste management.

Abstract

In this paper, we study the numerical approximation of a system of partial dif-ferential equations describing the corrosion of an iron based alloy in a nuclear waste repository. In particular, we are interested in the convergence of a numerical scheme consisting in an implicit Euler scheme in time and a Scharfetter-Gummel finite volume scheme in space.