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Finite difference analysis of a double‐porosity consolidation model
Author(s) -
Boal N.,
Gaspar F. J.,
Lisbona F. J.,
Vabishchevich P. N.
Publication year - 2012
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.20612
Subject(s) - consolidation (business) , mathematics , convergence (economics) , porosity , partial differential equation , finite element method , a priori and a posteriori , finite difference , numerical analysis , work (physics) , finite difference method , mathematical analysis , scheme (mathematics) , partial derivative , geotechnical engineering , geology , structural engineering , thermodynamics , philosophy , business , physics , accounting , epistemology , engineering , economics , economic growth
This work deals with the numerical solution of a two‐dimensional double‐porosity consolidation problem using a finite difference scheme. Stabilized discretizations using staggered grids in both space and time are proposed. A priori estimates for displacements and pressures in discrete energy norms are obtained, and the corresponding convergence results are given. Numerical examples illustrate the convergence properties of the proposed numerical scheme. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 138–154, 2012