Abstract
It is known that the non-smoothness of boundary data causes the order of convergence of the numerical solutions of partial differential equations [11] to be less than optimal. In this paper we assess the efect of mesh grading to overcome this difficulty in the context of the Boundary Element Method (BEM). As test cases we employed two potential problems proposed by Schultz [10]. We conclude that the BEM yields for a given mesh smaller errors than those obtained by the Finite Difference Methods (FDM) of [10], but at the expense of a greater computa tional effort. Also a judicious choice of mesh grading can improve significantly the actual error and recover the optimal order of convergence.
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© 1981 Springer-Verlag Berlin Heidelberg
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Pina, H.L.G., Fernandes, J.L.M., Brebbia, C.A. (1981). The Effect of Mesh Refinement in the Boundary Element Solution of Laplace’s Equation with Singularities. In: Brebbia, C.A. (eds) Boundary Element Methods. Boundary Elements, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11270-0_28
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DOI: https://doi.org/10.1007/978-3-662-11270-0_28
Publisher Name: Springer, Berlin, Heidelberg
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