A priori error estimates of two monolithic schemes for Biot's consolidation model

Gu，Huipeng1,2; Cai，Mingchao3; Li，Jingzhi4; Ju，Guoliang2

2023

10.1002/num.23059

Numerical Methods for Partial Differential Equations   Impact Factor & Quartile

0749-159X

1098-2426

This paper concentrates on a priori error estimates of two monolithic schemes for Biot's consolidation model based on the three-field formulation introduced by Oyarzúa et al. (SIAM J Numer Anal, 2016). The spatial discretizations are based on the Taylor–Hood finite elements combined with Lagrange elements for the three primary variables. We employ two different schemes to discretize the time domain. One uses the backward Euler method, and the other applies the combination of the backward Euler and Crank-Nicolson methods. A priori error estimates show that both schemes are unconditionally convergent with optimal error orders. Detailed numerical experiments are presented to validate the theoretical analysis.

a priori error estimates Biot's model finite element

SCI

English

First

NSF of China[11971221] ; Shenzhen Sci-Tech Fund["RCJC20200714114556020","JCYJ20170818153840322","JCYJ20190809150413261"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001] ; NIH-BUILD[UL1GM118973] ; NIH-RCMI[U54MD013376] ; National Science Foundation["1700328","1831950"] ; National Key R amp; D Program of China[2017YFB1001604]

Mathematics

Mathematics, Applied

WOS:001018437200001

WILEY

ENGINEERING

2-s2.0-85164192760

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
2.Department of High Performance Computing,National Supercomputing Center in Shenzhen,Shenzhen,China
3.Department of Mathematics,Morgan State University,Baltimore,United States
4.Department of Mathematics & National Center for Applied Mathematics Shenzhen & SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China

Gu，Huipeng,Cai，Mingchao,Li，Jingzhi,et al. A priori error estimates of two monolithic schemes for Biot's consolidation model[J]. Numerical Methods for Partial Differential Equations,2023.

Gu，Huipeng,Cai，Mingchao,Li，Jingzhi,&Ju，Guoliang.(2023).A priori error estimates of two monolithic schemes for Biot's consolidation model.Numerical Methods for Partial Differential Equations.

Gu，Huipeng,et al."A priori error estimates of two monolithic schemes for Biot's consolidation model".Numerical Methods for Partial Differential Equations (2023).