The convergence of spline collocation for strongly elliptic equations on curves
type: Item
instance of: scholarly article
title: The convergence of spline collocation for strongly elliptic equations on curves
zbMATH Open document ID: 0592.65077
DOI: 10.1007/BF01389582
author: Douglas N. Arnold
author: W. L. Wendland
published in: Numerische Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133036
review text: This paper presents a unified asymptotic error analysis for even as well as for odd degree splines subordinate. Uniform or smoothly graded meshes are in consideration only. The asymptotic convergence of optimal order is proved. The crucial assumption for the generalized boundary integral and integro- differential operators is strong ellipticity. The analysis is based on Fourier expansion, it extends known results to variable coefficient equations. This paper contains the first convergence proof of midpoint collocation with piecewise constant functions.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 3951943
zbMATH Keywords: asymptotic error analysis
zbMATH Keywords: smoothly graded meshes
zbMATH Keywords: asymptotic convergence
zbMATH Keywords: optimal order
zbMATH Keywords: Fourier expansion
zbMATH Keywords: collocation
MaRDI profile type: Publication
cites work: A Spline-Trigonometric Galerkin Method and an Exponentially Convergent Boundary Integral Method
cites work: On the Asymptotic Convergence of Collocation Methods
cites work: Q4124250
cites work: Piecewise Continuous Collocation for Integral Equations
cites work: Q3890616
cites work: Q3931209
cites work: Q3926025
cites work: Q3930771
cites work: Q3308996
cites work: Q3671071
cites work: Q3219912
cites work: Q3666156
cites work: Q3309241
cites work: Q3736253
cites work: Theoretical acoustics and numerical techniques
cites work: Procedures for kernel approximation and solution of Fredholm integral equations of the second kind
cites work: An Improved Method for Numerical Conformal Mapping
cites work: Simultaneous approximation in negative norms of arbitrary order
cites work: Fourier integral operators. I
cites work: Q3702476
cites work: Some applications of a galerkin‐collocation method for boundary integral equations of the first kind
cites work: Q4116031
cites work: Q3318255
cites work: On Local Approximation Properties of L2-Projection on Spline-Subspaces†
cites work: Interior Estimates for Ritz-Galerkin Methods
cites work: A Collection Method for the Numerical Solution of Integral Equations
cites work: Ein Lokalisierungsprinzip in der Theorie der Spline-Approximationen und einige Anwendungen
cites work: A spline collocation method for singular integral equations with piecewise continuous coefficients
cites work: Quadrature and collocation methods for singular integral equations on curves with corners
cites work: A Finite Element Collocation Method for Singular Integral Equations
cites work: Q3915982
cites work: An integral equation approach to boundary value problems of classical elastostatics
cites work: On the Asymptotic Convergence of Collocation Methods With Spline Functions of Even Degree
cites work: The fourier series representation of pseudo-differentiai operators on closed curves
cites work: On Spline Collocation for Singular Integral Equations
cites work: On spline collocation methods for boundary integral equations in the plane
cites work: The convergence of Galerkin and collocation methods with splines for pseudodifferential equations on closed curves
cites work: Q5522602
cites work: Integral equation methods in potential theory. II
cites work: Q3900552
OpenAlex ID: W2153780713
description: scientific article; zbMATH DE number 3951943