Journal of Integral Equations and Applications · 1993 · 15 citations · 2 references
ComputingComputer ScienceComputational GeometryComputational PhysicsScientific ComputingIntegral Equation FormulationsIntegral EquationsNumerical AnalysisNumerical IntegrationNumerical Methods For Differential EquationsSurface InterpolationHigh-order Numerical IntegrationNumerical Methods For Integral EquationsPiecewise Polynomial ApproximationPiecewise Polynomial InterpolationPolynomial InterpolationPolynomial Surface InterpolationSurface Integral Equations
We consider solving integral equations on a piecewise smooth surface S in R 3 with a smooth kernel function, using piecewise polynomial collocation interpolation of the surface. The theoretical analysis includes the effects of the numerical integration of the collocation coefficients and the use of the approximating surface. The resulting order of convergence is higher than had previously been expected in the literature.
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