Saranen, J.; Wendland, W. L. On the asymptotic convergence of collocation methods with spline functions of even degree. (English) Zbl 0623.65145 Math. Comput. 45, 91-108 (1985). The authors investigate the asymptotic convergence of the collocation method using even-degree polynomial splines applied to strongly elliptic systems of pseudo-differential equations on closed curves with convolutional principal part. The method is equivalent to a version of the Petrov-Galerkin method and allows to state the Babuška stability condition. Optimal error estimates on the scale of Sobolev spaces are given. Reviewer: G.Vainikko Cited in 36 Documents MSC: 65R20 Numerical methods for integral equations 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 45K05 Integro-partial differential equations 35S15 Boundary value problems for PDEs with pseudodifferential operators 74S30 Other numerical methods in solid mechanics (MSC2010) Keywords:asymptotic convergence; collocation method; polynomial splines; strongly elliptic systems; convolutional principal part; Petrov-Galerkin method; Babuška stability condition; Optimal error estimates; Sobolev spaces PDF BibTeX XML Cite \textit{J. Saranen} and \textit{W. L. Wendland}, Math. Comput. 45, 91--108 (1985; Zbl 0623.65145) Full Text: DOI EuDML OpenURL