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Document type:
Konferenzbeitrag 
Contribution type:
Textbeitrag / Aufsatz 
Author(s):
Bompadre, A.; Perotti, L.E.; Cyron, C.J.; Ortiz, M. 
Title:
HOLMES: convergent meshfree approximation schemes of arbitrary order and smoothness 
Abstract:
Local Maximum-Entropy (LME) approximation schemes are meshfree approximation schemes that satisfy consistency conditions of order one, i. e., they approximate affine functions exactly. In addition, LME approximation schemes converge in the Sobolev space W^1,p, i. e., they are C^0-continuous in the conventional terminology of finite-element interpolation. Here we present a generalization of the Local Max-Ent approximation schemes that are consistent to arbitrary order, i. e., interpolate polynomials of arbitrary degree exactly, and which converge in W^(k,p), i. e., they are C^k-continuous to arbitrary order k. We refer to these approximation schemes as High Order Local Maximum-Entropy Approximation Schemes (HOLMES). We prove uniform error bounds for the HOLMES approximates and their derivatives up to order k. Moreover, we show that the HOLMES of order k is dense in the Sobolev Space W^(k,p), for any 1 le p < infty. The good performance of HOLMES relative to other meshfree schemes in selected test cases is also critically appraised. 
Keywords:
high-order meshfree interpolation 
Dewey Decimal Classification:
620 Ingenieurwissenschaften 
Book / Congress title:
6th International Workshop Meshfree Methods for Partial Differential Equations 
Publisher address:
Bonn, Germany 
Year:
2011 
Reviewed:
ja 
Language:
en 
Publication format:
Print 
Semester:
WS 11-12 
Format:
Text