Abstract
This paper is concerned with the numerical solution of boundary integral equations on smooth curves of the plane with some numerical methods having in common the use of sets of equally spaced periodic Dirac delta distributions as trial functions. In a functional frame of classical periodic pseudodifferential equations of nonpositive order, delta-spline and delta–delta methods are introduced and analysed with the overall aim of obtaining asymptotic expansions of the error in weak and strong norms. As a byproduct we obtain the convergence of the coefficients associated to the discrete delta approximation to pointwise values of the unknown, as well as superconvergent choices of positions of the delta distributions in relation with the discretization grid. Two numerical examples are explored to show nodal errors and the applicability of Richardson extrapolation.
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Celorrio, R., Domínguez, V. & Sayas, FJ. Periodic Dirac Delta Distributions in the Boundary Element Method. Advances in Computational Mathematics 17, 211–236 (2002). https://doi.org/10.1023/A:1016002302671
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DOI: https://doi.org/10.1023/A:1016002302671