On semi-infinite spectral elements for Poisson problems with re-entrant boundary singularities

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A spectral element method is described which enables Poisson problems defined in irregular infinite domains to be solved as a set of coupled problems over semi-infinite rectangular regions. Two choices of trial functions are considered, namely the eigenfunctions of the differential operator and Chebyshev polynomials. The coefficients in the series expansions are obtained by imposing weak C1 matching conditions across element interfaces. Singularities at re-entrant corners are treated by a post-processing technique which makes use of the known asymptotic behaviour of the solution at the singular point. Accurate approximations are obtained with few degrees of freedom.

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论文评审过程:Received 11 December 1986, Revised 15 July 1987, Available online 22 March 2002.

论文官网地址:https://doi.org/10.1016/0377-0427(88)90266-X