A Petrov–Galerkin method with quadrature for elliptic boundary value problems

We propose and analyse a fully discrete Petrov–Galerkin method with quadrature, for solving second‐order, variable coefficient, elliptic boundary value problems on rectangular domains. In our scheme, the trial space consists of C2 splines of degree r ≥ 3, the test space consists of C0 splines of deg...

Full description

Saved in:
Bibliographic Details
Published in:IMA journal of numerical analysis 2004-01, Vol.24 (1), p.157-177
Main Authors: Bialecki, B., Ganesh, M., Mustapha, K.
Format: Article
Language:English
Subjects:
Boundary value problems
elliptic boundary value problems
Exact sciences and technology
Gauss quadrature
Mathematical analysis
Mathematics
Partial differential equations
Petrov–Galerkin method
Sciences and techniques of general use
splines
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose and analyse a fully discrete Petrov–Galerkin method with quadrature, for solving second‐order, variable coefficient, elliptic boundary value problems on rectangular domains. In our scheme, the trial space consists of C2 splines of degree r ≥ 3, the test space consists of C0 splines of degree r − 2, and we use composite (r − 1)‐point Gauss quadrature. We show existence and uniqueness of the approximate solution and establish optimal order error bounds in H2, H1 and L2 norms.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/24.1.157