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Boundary layer approximate approximations and cubature of potentials in domains. (English) Zbl 0935.65128
The authors present a new approach to the computation of volume potentials over bounded domains. It is based on quasi-interpolation with smooth, almost locally supported basis functions for which particular solutions are known. Some asymptotic error estimates for quasi-interpolation and corresponding cubature formulae as well as numerical examples which illustrate the behaviour of the error near the boundary are carried out.

65N38 Boundary element methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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