TY - JOUR

T1 - Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes

AU - Abarbanel, Saul

AU - Ditkowski, Adi

N1 - 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.

PY - 1997/5/15

Y1 - 1997/5/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031570221&partnerID=8YFLogxK

U2 - 10.1006/jcph.1997.5653

DO - 10.1006/jcph.1997.5653

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AN - SCOPUS:0031570221

VL - 133

SP - 279

EP - 288

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -