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Convergence of corrected derivative methods for second-order linear partial differential equations

✍ Scribed by T. Black; T. Belytschko

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 224 KB
Volume: 44
Category: Article
ISSN: 0029-5981
DOI: 10.1002/(sici)1097-0207(19990120)44:2<177::aid-nme498>3.0.co;2-1

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✦ Synopsis

Approximations where the derivatives are corrected so as to satisfy linear completeness on the derivatives are investigated. These techniques are used in particle methods and other mesh-free methods. The basic approximation is a Shepard interpolant which possesses only constant completeness. The derivatives are then corrected to meet linear completeness conditions. It is shown that the resulting methods have order h convergence in the energy and L 2 norms. The proof is subject to an inf-sup condition which is studied numerically. Numerical studies of the Poisson equation verify the convergence estimates.

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