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BIT Numerical Mathematics

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04-10-2016

Quasi-interpolation based on the ZP-element for the numerical solution of integral equations on surfaces in \(\mathbb {R}^3\)

Authors: Catterina Dagnino, Sara Remogna

Published in: BIT Numerical Mathematics | Issue 2/2017

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Abstract

The aim of this paper is to present spline methods for the numerical solution of integral equations on surfaces of \(\mathbb {R}^3\), by using optimal superconvergent quasi-interpolants defined on type-2 triangulations and based on the Zwart–Powell quadratic box spline. In particular we propose a modified version of the classical collocation method and two spline collocation methods with high order of convergence. We also deal with the problem of approximating the surface. Finally, we study the approximation error of the above methods together with their iterated versions and we provide some numerical tests.

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Title: Quasi-interpolation based on the ZP-element for the numerical solution of integral equations on surfaces in
Authors: Catterina Dagnino
Sara Remogna
Publication date: 04-10-2016
Publisher: Springer Netherlands
Published in: BIT Numerical Mathematics / Issue 2/2017
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-016-0633-x

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