Finite elements for the space approximation of a differential model for salts crystallization

TL;DR

This paper develops a finite element numerical method for simulating salt crystallization in stone degradation, extending previous one-dimensional models to higher dimensions with stability analysis and experimental convergence validation.

Contribution

It introduces a finite element space discretization and implicit-explicit time marching scheme for a salt crystallization model, enabling realistic multi-dimensional simulations.

Findings

Stable numerical scheme with convergence properties

Effective simulation of salt crystallization in 2D and 3D

Performance validated through numerical experiments

Abstract

This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A numerical method based on finite-element space discretization and implicit-explicit time marching is proposed as an extension of a one-dimensional finite-difference framework introduced in the literature. Within the same one-dimensional setting, a sensitivity analysis is performed, based on the techniques developed therein. They are also used as a comparison tool for the finite-element formulation, here introduced for more realistic simulations in higher space dimensions. Considerations about stability will be provided, together with an experimental convergence analysis highlighting the performance of the proposed approach. Numerical results in two and three space dimensions, obtained by an efficient code implementation, will be presented and discussed.