Startseite Sharp geometric requirements in the Wachspress interpolation error estimate
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Sharp geometric requirements in the Wachspress interpolation error estimate

  • Gabriel Monzón EMAIL logo
Veröffentlicht/Copyright: 28. Juni 2017
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Abstract

Geometric conditions on general polygons are given in [9] in order to guarantee the error estimate for interpolants built from generalized barycentric coordinates, and the question about identifying sharp geometric restrictions in this setting is proposed. In this work, we address the question when the construction is made by using Wachspress coordinates. We basically show that the imposed conditions bounded aspect ratio property (barp), maximum angle condition (MAC) and minimum edge length property (melp) are actually equivalent to (MAC, melp), and if any of these conditions is not satisfied, then there is no guarantee that the error estimate is valid. In this sense, (MAC) and (melp) can be regarded as sharp geometric requirements in the Wachspress interpolation error estimate.

MSC 2010: 65N15; 65N30

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Received: 2016-7-12
Revised: 2017-6-5
Accepted: 2017-6-7
Published Online: 2017-6-28
Published in Print: 2018-1-1

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