A Schwarz alternating procedure using spline collocation methods

Autor:	Elizabeth Greenwell Yanik
Rok vydání:	1989
Předmět:	Numerical Analysis Collocation Maximum principle Partial differential equation Rate of convergence Applied Mathematics Collocation method Mathematical analysis General Engineering Orthogonal collocation Rectangle Schwarz alternating method Mathematics
Zdroj:	International Journal for Numerical Methods in Engineering. 28:621-627
ISSN:	1097-0207 0029-5981
DOI:	10.1002/nme.1620280310
Popis:	A collocation method is described which obtains an approximate solution to Poisson's equation, δu = f, on an L shaped region. The L shaped region is viewed as the union of two overlapping rectangles. The Schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle. The convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods. Several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the L shaped region.
Databáze:	OpenAIRE
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