Convergence of approximate solutions constructed by the finite volume method for the moisture transport model in porous media

TL;DR

This paper proves the convergence of finite volume method solutions for a nonlinear moisture transport model in porous media, ensuring the reliability of numerical approximations for this class of problems.

Contribution

It establishes the convergence of finite volume solutions and proves uniqueness of weak solutions for a nonlinear moisture transport equation.

Findings

Convergence of finite volume solutions is rigorously proven.

Uniqueness of weak solutions is established.

The model accurately describes moisture transport in porous media.

Abstract

We consider the initial-boundary value problem for a nonlinear parabolic equation in the one-dimensional interval. This problem is motivated by a mathematical model for moisture transport in porous media. We establish the uniqueness of weak solutions to the problem by using the dual equation method. Moreover, we prove the convergence of approximate solutions constructed with the finite volume method.