A spline collocation method for parabolic pseudodifferential equations

Anttila, Juha

doi:10.1016/s0377-0427(01)00401-0

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2007

2015

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By using a variant of the Arnold-Wendland Lemma we are able to show that the collocation solution is stable and give asymptotic convergence results. In [1] and [2] some suboptimal convergence results is shown in unconventional Sobolev spaces.…”

Section: Introductionmentioning

confidence: 99%

The boundary element spline collocation for nonuniform meshes on the torus

Saranen

Anttila

2007

Numer. Math.

View full text Add to dashboard Cite

The spline collocation method for a class of biperiodic strongly elliptic pseudodifferential operators is considered. 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. It is shown that the collocation problem is uniquely solvable if the maximum mesh length is small enough. Moreover, the approximation is stable and quasioptimal with respect to a norm depending on the order of the operator and the degree of approximating splines. Some convergence results are given for general and quasiuniform meshes. The results cover for example the single layer and the hypersingular operators.

show abstract

Section: Introductionmentioning

confidence: 99%