Boundary layer approximate approximations and cubature of potentials in domains |
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Authors: | Ivanov Tjavdar Mazya Vladimir Schmidt Gunther |
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Institution: | 1.Department of Mathematics, Linköping University, S‐581 83, Linköping, Sweden ;2.Weierstraß Institute of Applied Analysis and Stochastics, Mohrenstr. 39, D‐10117, Berlin, Germany ; |
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Abstract: | In this article we present a new approach to the computation of volume potentials over bounded domains, which is based on
the quasi‐interpolation of the density by almost locally supported basis functions for which the corresponding volume potentials
are known. The quasi‐interpolant is a linear combination of the basis function with shifted and scaled arguments and with
coefficients explicitly given by the point values of the density. Thus, the approach results in semi‐analytic cubature formulae
for volume potentials, which prove to be high order approximations of the integrals. It is based on multi‐resolution schemes
for accurate approximations up to the boundary by applying approximate refinement equations of the basis functions and iterative
approximations on finer grids. We obtain asymptotic error estimates for the quasi‐interpolation and corresponding cubature
formulae and provide some numerical examples.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | volume potentials semi‐ analytic cubature formulae approximate approximations approximate multi‐ resolution 65D32 65D15 65N38 |
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