Defect correction and domain decomposition for second-order boundary value problems

Highly accurate approximation is obtained through the techniques of defect correction and domain decomposition for second-order elliptic boundary value problems on a disc. The basic solution is computed using the Schwarz domain decomposition procedure and bilinear Galerkin finite element approximati...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 130; no. 1; pp. 41 - 51
Main Author: Chibi, Ahmed-Salah
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.05.2001
Elsevier
Subjects:
Acceleration of convergence
Bilinear finite elements
Defect correction
Elliptic problems
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Schwarz domain decomposition
Sciences and techniques of general use
Bilinear finite elements
Defect correction
65J10
Elliptic problems
65B05
65N55
Schwarz domain decomposition
65N30
Second order
Bilinear system
Partial differential equation
Finite element method
Boundary value problem
Schwarz mzthod
Elliptic problem
Lagrange interpolation
Defect
Galerkin method
Domain decomposition
Corrections
Finite element
Bilinear approximation
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:Highly accurate approximation is obtained through the techniques of defect correction and domain decomposition for second-order elliptic boundary value problems on a disc. The basic solution is computed using the Schwarz domain decomposition procedure and bilinear Galerkin finite element approximation on each subdomain to get an O( h 2) accurate basic solution in higher-order discrete Sobolev norms. The defects are then computed using high-order polynomials (Lagrange polynomials or splines) to get as many O( h 2) corrections as possible.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(99)00392-1