Improved accuracy in finite element analysis of Biot's consolidation problem
Computer Methods in Applied Mechanics and Engineering
Asymptotic behavior of semidiscrete finite-element approximations of Biot's consolidation problem
SIAM Journal on Numerical Analysis
A finite difference analysis of Biot's consolidation model
Applied Numerical Mathematics
Multigrid relaxation methods for systems of saddle point type
Applied Numerical Mathematics
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Finite difference methods for a two-dimensional quasi-static Biot's consolidation problem are considered. Stabilized space discretization using staggered grids and the implicit Euler scheme for time stepping is proposed. A priori estimates for displacements and pressure in discrete energy norms are obtained and the corresponding convergence results are proved. Numerical examples are given to illustrate the convergence properties of these stabilized methods.