, Volume 46, Issue 4, pp 505-520

Spectral methods for exterior elliptic problems

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This paper deals with spectral approximations for exterior elliptic problems in two dimensions. As in the conventional finite difference or finite element methods, it is found that the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. We introduce a spectral boundary treatment at infinity, which is compatible with the “infinite order” interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although we deal with a simple Laplace problem throughout the paper, our analysis covers more complex and general cases.

Research for the first author was supported by NASA Contract No. NAS1-17070 and for the second author by NASA Contract No. NAS1-17130 while both were in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665, USA