Spline approximation methods for multidimensional periodic pseudodifferential equations

Autor:	Siegfried Prössdorf, Reinhold Schneider
Rok vydání:	1992
Předmět:	Algebra and Number Theory Numerical analysis Mathematical analysis Triangular grid Integral equation Mathematics::Numerical Analysis law.invention Spline (mathematics) Invertible matrix M-spline law Collocation method Galerkin method Analysis Mathematics
Zdroj:	Integral Equations and Operator Theory. 15:626-672
ISSN:	1420-8989 0378-620X
DOI:	10.1007/bf01195782
Popis:	We investigate several numerical methods for solving the pseudodifferential equationAu=f on the n-dimensional torusT n . We examine collocation methods as well as Galerkin-Petrov methods using various periodical spline functions. The considered spline spaces are subordinated to a uniform rectangular or triangular grid. For given approximation method and invertible pseudodifferential operatorA we compute a numerical symbolα C , resp.α G , depending onA and on the approximation method. It turns out that the stability of the numerical method is equivalent to the ellipticity of the corresponding numerical symbol. The case of variable symbols is tackled by a local principle. Optimal error estimates are established.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::84ed2af9bd7851b32af5ff9e0a1d9c9a https://doi.org/10.1007/bf01195782 Zobrazit plný text záznamu Full text from SpringerLink