An initial-boundary value problem describing moisture transport in porous media: existence of strong solutions and an error estimate for a finite volume scheme

TL;DR

This paper proves the existence of strong solutions for a moisture transport model in porous media and provides an error estimate for a finite volume numerical scheme, using advanced inequalities.

Contribution

It establishes the existence of strong solutions and derives an error estimate for the finite volume method applied to moisture transport in porous media.

Findings

Existence of strong solutions for the model

Error bounds for the finite volume scheme

Use of Gagliardo--Nirenberg inequality in analysis

Abstract

We consider an initial-boundary value problem motivated by a mathematical model of moisture transport in porous media. We establish the existence of strong solutions and provide an error estimate for the approximate solutions constructed by the finite volume method. In the proof of the error estimate, the Gagliardo--Nirenberg type inequality for the difference between a continuous function and a piecewise constant function plays an important role.