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A stabilized method for a secondary consolidation Biot's model
Author(s) -
Gaspar F.J.,
Gracia J.L.,
Lisbona F.J.,
Vabishchevich P.N.
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20242
Subject(s) - biot number , discretization , mathematics , consolidation (business) , convergence (economics) , finite difference , a priori and a posteriori , numerical analysis , finite element method , mathematical analysis , work (physics) , partial differential equation , mechanics , philosophy , physics , accounting , epistemology , economics , business , thermodynamics , economic growth , mechanical engineering , engineering
This work deals with the numerical solution of a secondary consolidation Biot's model. A family of finite difference methods on staggered grids in both time and spatial variables is considered. These numerical methods use a weighted two‐level discretization in time and the classical central difference discretization in space. A priori estimates and convergence results for displacements and pressure in discrete energy norms are obtained. Numerical examples illustrate the convergence properties of the proposed numerical schemes, showing also a non‐oscillatory behavior of the pressure approximation. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007