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.