Solving parabolic problems using local defect correction in combination with the finite volume method | Zendy

Minero R. | Zendy; Anthonissen M.J.H. | Zendy; Mattheij R.M.M. | Zendy

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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

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