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In this paper, the combination of the h‐method (mesh refinement) and the r‐method (mesh redistribution) is employed to solve the Laplace equation using the boundary element procedure. The key in this approach is to derive on upper bound for the residual associated with the boundary element solution and minimize this bound with respect to an unknown grading function. The latter part is achieved by employing techniques of the calculus of variations. Copyright © 1992 John Wiley & Sons, Ltd