A fourth order accurate difference-analytical method for solving Laplace’s boundary value problem with singularities
High accurate difference-analytical method of solving the mixed boundary value problem for Laplace’s equation on graduated polygons (which can have broken sections and be multiply connected) is described and justified. The uniform estimate for the error of the approximate solution is of order O(h 4), where h is the mesh step, for the errors of derivatives of order p, p = 1, 2, ..., in a finite neighbourhood of re-entrant vertices, of order O(h 4/r j p−λj ), where r j is the distance from the current point to the vertex in question, λ j = 1/α j or λ j = 1/2α j depending on the types of boundary conditions, α j π is the value of the angle. The last part of the paper is devoted to illustrate numerical experiments.
KeywordsStress Intensity Factor Fourth Order Laplace Equation Uniform Estimate Mixed Boundary
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