A finite volume scheme for solving elliptic boundary value problems on composite grids

M.J.H. Anthonissen, B. Hof, van 't, A.A. Reusken

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6 Citations (Scopus)

Abstract

We present a finite volume scheme for solving elliptic boundary value problems with solutions that have one or a few small regions with high activity. The scheme results from combining the local defect correction method (LDC), introduced in [11], with standard finite volume discretizations on a global coarse and on local fine uniform grids. The iterative discretization method that is obtained in this way yields a discrete approximation of the continuous solution on a composite grid. For the LDC method in its standard form, the discrete conservation property, which is one of the main attractive features of a finite volume method, is lost for the composite grid approximation. For the modified LDC method we present here, discrete conservation holds for the composite grid solution, too.
Original languageEnglish
Pages (from-to)285-305
Number of pages21
JournalComputing
Volume61
Issue number4
DOIs
Publication statusPublished - 1998

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