Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes

Saul Abarbanel, Adi Ditkowski

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44 Scopus citations


An algorithm which solves the multidimensional diffusion equation on complex shapes to fourth-order accuracy and is asymptotically stable in time is presented. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty-like terms. Numerical examples in 2-D showthatthe method is effective even where standard schemes, stable by traditional definitions, fail. The ability of the paradigm to be applied to arbitrary geometric domains is an important feature of the algorithm.

Original languageEnglish
Pages (from-to)279-288
Number of pages10
JournalJournal of Computational Physics
Issue number2
StatePublished - 15 May 1997
Externally publishedYes

Bibliographical note

Funding Information:
1This research was supported by the National Aeronautics and Space Administration under NASA Contract NAS1-19480 while the authors were in the residence of the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA. S. Abarbanel was also supported in part by the Air Force Office of Scientific Research under Grant AFOSR-F49620-95-1-0074, and by the Department of Energy under Grant DOE-DE-FG02-95ER25239.


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