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Boundary element collocation methods using splines with multiple knots

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We extend the theory of boundary element collocation methods by allowing reduced inter-element smoothness (or in other words, by allowing trial functions that are splines with multiple knots). Our convergence analysis is based on a recurrence relation for the Fourier coefficients of the numerical solution, and so is restricted to uniform grids on smooth, closed curves. Superconvergence is possible with special choices of the collocation points. Numerical experiments with a model problem confirm the convergence rates predicted by our theory.

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Received September 19, 1995

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McLean, W., Prößdorf, S. Boundary element collocation methods using splines with multiple knots . Numer. Math. 74, 419–451 (1996). https://doi.org/10.1007/s002110050224

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  • Mathematics Subject Classification (1991): 65N38, 41A15, 65N12, 35S99, 42A16