# Asymptotic behavior of semidiscrete finite-element approximations of Biot's consolidation problem

@article{Murad1996AsymptoticBO, title={Asymptotic behavior of semidiscrete finite-element approximations of Biot's consolidation problem}, author={Marcio A. Murad and Vidar Thom{\'e}e and Abimael Fernando Dourado Loula}, journal={SIAM Journal on Numerical Analysis}, year={1996}, volume={33}, pages={1065-1083} }

Error estimates for spatially discrete Galerkin finite-element approximations of Biot’s model for consolidation of saturated porous media are presented. The short- and long-time behaviors of such approximations based on both stable and unstable combinations of finite-element spaces of displacement and pore pressure fields are discussed.

## 102 Citations

### Analysis of a discontinuous Galerkin method for the Biot's consolidation problem

- Computer ScienceAppl. Math. Comput.
- 2013

### Finite Difference Scheme for Filtration and Consolidation Problems

- Computer Science, MathematicsNumerical Methods and Application
- 2002

A monotone and second order finite difference scheme on this kind of grid is given and some numerical results show that this scheme stabilizes the Biot's consolidation problem.

### Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements

- MathematicsAdvances in Applied Mathematics and Mechanics
- 2018

Abstract. Using the standard mixed Galerkin methods with equal order elements to solve Biot’s consolidation problems, the pressure close to the initial time produces large non-physical oscillations.…

### Weak Galerkin finite element method for Biot's consolidation problem

- Computer ScienceJ. Comput. Appl. Math.
- 2018

### Analysis and preconditioning of parameter-robust finite element methods for Biot's consolidation model

- Computer Science
- 2018

A three-field formulation of the Biot model which has the displacement, the total pressure, and the pore pressure as unknowns is considered, and a priori estimates of the continuous problem with parameter-dependent norms are shown.

### Stability and monotonicity for some discretizations of the Biot’s consolidation model

- Computer Science
- 2016

### Finite element method with the total stress variable for Biot's consolidation model

- GeologyNumerical Methods for Partial Differential Equations
- 2020

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…

### Robust estimates for the approximation of the dynamic consolidation problem

- Mathematics
- 2010

We consider stable discretizations in time and space for the linear dynamic consolidation problem describing wave propagation in a porous solid skeleton that is fully saturated with an incompressible…

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