Robust virtual element methods for 3D stress-assisted diffusion problems
Numerical Analysis
2025-02-05 v1 Numerical Analysis
Abstract
This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended Babu\v{s}ka-Brezzi-Braess theory for perturbed saddle-point problems, and Banach fixed-point theory play a crucial role in performing a robust analysis of the fully coupled non-linear system. The proposed virtual element formulations are provided with appropriate projection, interpolation, and stabilisation operators that ensures the well-posedness of the discrete problem. Numerical simulations are conducted to show the accuracy, performance, and applicability of the method.
Cite
@article{arxiv.2502.01851,
title = {Robust virtual element methods for 3D stress-assisted diffusion problems},
author = {Andres E. Rubiano},
journal= {arXiv preprint arXiv:2502.01851},
year = {2025}
}