Interpolation properties of generalized plane waves

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• 作者：Lise-Marie Imbert-Gérard
• 关键词：65D05 ; 65N99
• 刊名：Numerische Mathematik
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：131
• 期：4
• 页码：683-711
• 全文大小：847 KB
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  32.Trefftz, E.:
• 作者单位：Lise-Marie Imbert-Gérard (1)
  
  1. Courant Institute of Mathematical Sciences, NYU, 251 Mercer Street, New York, NY, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Mathematics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  Numerical and Computational Methods
  Applied Mathematics and Computational Methods of Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：0945-3245

文摘

This paper is aimed at developing new shape functions adapted to the scalar wave equation with smooth (possibly vanishing) coefficients and investigates the numerical analysis of their interpolation properties. The interpolation is local, but high order convergence is shown with respect to the size of the domain considered. The new basis functions are then implemented in a numerical method to solve a scalar wave equation problem with a mixed boundary condition. The main theoretical result states that any given order of approximation can be achieved by an appropriate choice of parameters for the design of the shape functions. The convergence is studied with respect to the size of the domain, which is referred to in the literature as \(h\)-convergence. Mathematics Subject Classification 65D05 65N99