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Solving parabolic problems using local defect correction in combination with the finite volume method
Author(s) -
Minero R.,
Anthonissen M.J.H.,
Mattheij R.M.M.
Publication year - 2006
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.20143
Subject(s) - finite volume method , discretization , mathematics , grid , partial differential equation , feature (linguistics) , finite volume method for one dimensional steady state diffusion , regular grid , volume (thermodynamics) , finite difference method , mathematical analysis , numerical partial differential equations , geometry , mechanics , thermodynamics , physics , linguistics , philosophy
We present a method for solving partial differential equations characterized by highly localized properties in which the local defect correction (LDC) algorithm for time‐dependent problems is combined with a finite volume discretization. At each time step, LDC computes a numerical solution on a composite grid, a union of a global uniform coarse grid and a local uniform fine grid. The main feature of the method is that the discrete conservation property, typical of the finite volume approach is preserved on the composite grid. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006