Residual-based a posteriori error estimates of mixed methods for a three-field Biot's consolidation model

Yuwen Li; Ludmil T. Zikatanov

doi:10.1093/imanum/draa074

Residual-based a posteriori error estimates of mixed methods for a three-field Biot's consolidation model

Yuwen Li, Ludmil T. Zikatanov

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7 Scopus citations

Abstract

We present residual-based a posteriori error estimates of mixed finite element methods for the three-field formulation of Biot's consolidation model. The error estimator are upper and lower bounds of the space-time discretization error up to data oscillation. As a by-product, we also obtain a new a posteriori error estimate of mixed finite element methods for the heat equation.

Original language	English (US)
Pages (from-to)	620-648
Number of pages	29
Journal	IMA Journal of Numerical Analysis
Volume	42
Issue number	1
DOIs	https://doi.org/10.1093/imanum/draa074
State	Published - Jan 1 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Computational Mathematics
Applied Mathematics

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10.1093/imanum/draa074

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abstract = "We present residual-based a posteriori error estimates of mixed finite element methods for the three-field formulation of Biot's consolidation model. The error estimator are upper and lower bounds of the space-time discretization error up to data oscillation. As a by-product, we also obtain a new a posteriori error estimate of mixed finite element methods for the heat equation.",

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AB - We present residual-based a posteriori error estimates of mixed finite element methods for the three-field formulation of Biot's consolidation model. The error estimator are upper and lower bounds of the space-time discretization error up to data oscillation. As a by-product, we also obtain a new a posteriori error estimate of mixed finite element methods for the heat equation.

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Residual-based a posteriori error estimates of mixed methods for a three-field Biot's consolidation model

Abstract

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