The boundary element spline collocation for nonuniform meshes on the torus
type: Item
instance of: scholarly article
title: The boundary element spline collocation for nonuniform meshes on the torus
zbMATH Open document ID: 1119.65120
published in: Numerische Mathematik
publication date: 2007-05-10T00:00:00Z
review text: The paper is concerned with the boundary element spline collocation method on the torus for a class of strongly elliptic biperiodic pseudodifferential equations. This class includes the single layer and hypersingular operators. As trial functions tensor products of odd degree splines are used and the collocation is imposed at the nodal points of the tensor product mesh. The analysis of the method is based on a variant of the Arnold-Wendland Lemma. It is shown that if the maximum mesh length is small enough, the collocation problem has a unique solution. Moreover, the approximation is stable and quasioptimal with respect to a norm depending on the order of the operator and the degree of the splines. Asymptotic convergence results are given for general and quasiuniform meshes.
reviewed by: Ana M. Alonso Rodriguez
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35S15
zbMATH DE Number: 5151304
zbMATH Keywords: collocation methods
zbMATH Keywords: tensor product splines
zbMATH Keywords: strongly elliptic pseudodifferential operators
zbMATH Keywords: equations on torus
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: boundary element method
author: J. Saranen
author: Juha Anttila
MaRDI profile type: Publication
full work available at URL: s00211-006-0055-9
OpenAlex ID: W2030655833
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DOI: 10.1007/S00211-006-0055-9
description: scientific article; zbMATH DE number 5151304