Robust three-field finite element methods for Biot's consolidation model in poroelasticity
type: Item
instance of: scholarly article
title: Robust three-field finite element methods for Biot's consolidation model in poroelasticity
zbMATH Open document ID: 1428.65044
published in: BIT
publication date: 2018-06-26T00:00:00Z
review text: The article presents a numerical scheme for approximating the Biot's consolidation model. Besides medium displacement and fluid pressure, a third variable is introduced for the product of the permeability tensor and pressure gradient. The resulting three-field model is approximated in space by finite elements, based on Raviart-Thomas, piecewise constant and Mardal-Tai-Winther elements. The temporal approximation is based on the backward Euler scheme. Error analysis for the semi-discrete and fully discrete solutions are presented, which avoid using Gronwall's inequality and yield favourable error bounds. Moreover, the error bounds are uniformly bounded for arbitrarily large Lame coefficients and small storage coefficients.
reviewed by: Aziz Takhirov
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M22
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 6894728
zbMATH Keywords: poroelasticity
zbMATH Keywords: mixed method
zbMATH Keywords: error analysis
zbMATH Keywords: locking-free
author: Jeonghun Lee
MaRDI profile type: Publication
full work available at URL: s10543-017-0688-3
OpenAlex ID: W2765196163
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DOI: 10.1007/S10543-017-0688-3
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description: scientific article; zbMATH DE number 6894728