A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem

10/19/2020
by   F. Bertrand, et al.
0

A posteriori error estimates are constructed for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure. The discretization under focus is the H1(Ω)-conforming Taylor-Hood finite element combination, consisting of polynomial degrees k + 1 for the displacements and the fluid pressure and k for the total pressure. An a posteriori error estimator is derived on the basis of H(div)-conforming reconstructions of the stress and flux approximations. The symmetry of the reconstructed stress is allowed to be satisfied only weakly. The reconstructions can be performed locally on a set of vertex patches and lead to a guaranteed upper bound for the error with a constant that depends only on local constants associated with the patches and thus on the shape regularity of the triangulation. Particular emphasis is given to nearly incompressible materials and the error estimates hold uniformly in the incompressible limit. Numerical results on the L-shaped domain confirm the theory and the suitable use of the error estimator in adaptive strategies.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 15

11/20/2019

Residual-based a posteriori error estimates of mixed methods in Biot's consolidation model

We present residual-based a posteriori error estimates of mixed finite e...
09/24/2021

A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method

We present an a posteriori error estimate based on equilibrated stress r...
02/23/2022

A posteriori error estimates for Darcy-Forchheimer's problem

This work deals with the a posteriori error estimates for the Darcy-Forc...
11/26/2021

Analysis of Mixed Finite Elements for Elasticity. I. Exact stress symmetry

We consider mixed finite element methods with exact symmetric stress ten...
06/16/2021

Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling

We develop the a posteriori error analysis of three mixed finite element...
09/04/2019

An equilibrated a posteriori error estimator for arbitrary-order Nédélec elements for magnetostatic problems

We present a novel a posteriori error estimator for Nédélec elements for...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.