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. 

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

Finite Difference Scheme for Filtration and Consolidation Problems

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

  • Gang Feng
  • Mathematics
    Advances 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.

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

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.

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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

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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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