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- Title
Supraconvergence of a finite difference scheme for solutions in H<sup>s</sup>(0, L).
- Authors
Barbeiro, S.; Ferreira, J. A.; Grigorieff, R. D.
- Abstract
In this paper we study the convergence of a centred finite difference scheme on a non-uniform mesh for a 1D elliptic problem subject to general boundary conditions. On a non-uniform mesh, the scheme is, in general, only first-order consistent. Nevertheless, we prove for s ∈ (1/2, 2] order O(hs)-convergence of solution and gradient if the exact solution is in the Sobolev space H1+s(0, L), i.e. the so-called supraconvergence of the method. It is shown that the scheme is equivalent to a fully discrete linear finite-element method and the obtained convergence order is then a superconvergence result for the gradient. Numerical examples illustrate the performance of the method and support the convergence result.
- Subjects
STOCHASTIC convergence; MATHEMATICAL functions; FINITE element method; NUMERICAL analysis; MATHEMATICAL analysis
- Publication
IMA Journal of Numerical Analysis, 2005, Vol 25, Issue 4, p797
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/dri018