Wigley, Neil M. An efficient method for subtracting off singularities at corners for Laplace’s equation. (English) Zbl 0657.65129 J. Comput. Phys. 78, No. 2, 369-377 (1988). The author derives a formula for the coefficients of an asymptotic expansion of the solution of Laplace’s equation near a singularity like a corner or a point of change of type of the boundary conditions. The approach is then as follows: The solution is approximated by discretization, the coefficients of a finite part of the series are found (by computing certain line integrals of the solution along a part of a circle) and the series is subtracted (which means essentially modifying the boundary conditions). This process is repeated iteratively. Finally, the series is added to the modified solution. Computational results are given for a number of problems. A comparison with the adaptive multigrid code PLTMG of R. E. Bank [PLTMG user’s guide: Dept. of Math., University of California at San Diego, CA (1985)] results are better by one-two orders of accuracy. Reviewer: G.Stoyan Cited in 18 Documents MSC: 65Z05 Applications to the sciences 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:harmonic functions; corner singularity; numerical example; asymptotic expansion; Laplace’s equation; comparison; adaptive multigrid code PLTMG PDFBibTeX XMLCite \textit{N. M. Wigley}, J. Comput. Phys. 78, No. 2, 369--377 (1988; Zbl 0657.65129) Full Text: DOI References: [1] Bank, R. E., (PLTMG User’s Guide (1985), Dept. of Math., University of California at San Diego: Dept. of Math., University of California at San Diego CA), (unpublished) [2] Fix, G. J.; Gulati, S.; Wakoff, G. I., J. Comput. Phys., 13, 209 (1973) [3] Gregory, J. A.; Fishelov, D.; Schiff, B.; Whiteman, J. R., J. Comput. Phys., 29, 133 (1978) [4] Henshell, R. D.; Shaw, K. G., Int. J. Numer. Methods Eng., 9, 495 (1975) [5] Li, Z.-C., J. Approx. Theory, 39, 132 (1983) [6] Thatcher, R. W., Numer. Math., 25, 179 (1976) [7] Wait, R., J. Inst. Math. its Appl., 20, 133 (1977) [8] Whiteman, J. R., Quart. J. Mech. Appl, Math., 21, 41 (1968) [9] Whiteman, J. R.; Papamichael, N., Z. Angew. Math. Phys., 23, 655 (1972) [10] Wigley, N. M., SIAM J. Numer. Anal., 24, 350 (1987) [11] Xanthis, L. S.; Bernal, M. J.M.; Atkinson, C., Comput. Methods Appl. Mech. Eng., 26, 285 (1981) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.