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A multidomain spectral approximation of elliptic equations
Author(s) -
Funaro Daniele
Publication year - 1986
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690020304
Subject(s) - mathematics , discretization , rectangle , convergence (economics) , rate of convergence , domain (mathematical analysis) , poisson's equation , mathematical analysis , legendre polynomials , stability (learning theory) , boundary value problem , matrix (chemical analysis) , domain decomposition methods , spectral method , finite element method , geometry , channel (broadcasting) , materials science , machine learning , economics , composite material , thermodynamics , economic growth , physics , engineering , computer science , electrical engineering
A spectral approximation for the Poisson equation defined on Ω = ]−1, 1[×] −1,1[ is studied. The domain Ω is decomposed into two rectangular regions and the equation is collocated at the Legendre nodes in each domain. On the common boundary of the two subdomains, suitable conditions are imposed in order to obtain a unique solution from the resulting linear system. Different values of the discretization parameters are allowed in each rectangle. We prove the stability of the scheme and give convergence estimates. The rate of convergence in a single subdomain, depends only on the regularity of the exact solution therein. An efficient preconditioning matrix is proposed.