On the asymptotic convergence of collocation methods with spline functions of even degree. (English) Zbl 0623.65145

Saranen, J.; Wendland, W. L.

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

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