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Finite element method with the total stress variable for Biot's consolidation model
Author(s) -
Qi Wenya,
Seshaiyer Padmanabhan,
Wang Junping
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22721
Subject(s) - biot number , mathematics , discretization , finite element method , consolidation (business) , backward euler method , mixed finite element method , convergence (economics) , rate of convergence , mathematical analysis , mechanics , computer science , structural engineering , physics , engineering , accounting , economics , business , economic growth , computer network , channel (broadcasting)
In this work, semi‐discrete and fully discrete error estimates are derived for the Biot's consolidation model described using a three‐field finite element formulation. These fields include displacements, total stress and pressure. The model is implemented using a backward Euler discretization in time for the fully discrete scheme and validated for benchmark examples. Computational experiments are presented to verify the convergence orders for two finite elements with discontinuous and continuous approximations for the total stress.