A priori error estimates of two fully discrete coupled schemes for Biot's consolidation model
Numerical Analysis
2022-11-22 v1 Numerical Analysis
Abstract
This paper concentrates on a priori error estimates of two fully discrete coupled schemes for Biot's consolidation model based on the three-field formulation introduced by Oyarzua et al. (SIAM Journal on Numerical Analysis, 2016). The spatial discretizations are based on the Taylor-Hood finite elements combined with Lagrange elements for the three primary variables. For time discretization, we consider two methods. One uses the backward Euler method, and the other applies a combination of the backward Euler and Crank-Nicolson methods. A priori error estimates show that the two schemes are unconditionally convergent with optimal error orders. Detailed numerical experiments are presented to validate the theoretical analysis.
Keywords
Cite
@article{arxiv.2211.10758,
title = {A priori error estimates of two fully discrete coupled schemes for Biot's consolidation model},
author = {Huipeng Gu and Mingchao Cai and Jingzhi Li and Guoliang Ju},
journal= {arXiv preprint arXiv:2211.10758},
year = {2022}
}