English

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}
}