Nejmeddine Chorfi, Mohamed Jleli
Abstract:
In a polygonal domain, the solution of a linear elliptic problem is written
as a sum of a regular part and a linear combination of singular functions
multiplied by appropriate coefficients. For computing the leading singularity
coefficient we use the dual method which based on the first singular dual
function. Our aim in this paper is the approximation of this leading
singularity coefficient by spectral element method which relies on the
mortar decomposition domain technics. We prove an optimal error estimate
between the continuous and the discrete singularity coefficient.
We present numerical experiments which are in perfect coherence with the analysis.
Submitted April 5, 2015. Published June 12, 2015.
Math Subject Classifications: 35J15, 78M22.
Key Words: Mortar spectral method; singularity; crack.
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Nejmeddine Chorfi Department of Mathematics College of Science, King Saud University P.O. Box 2455, Riyadh 11451, Saudi Arabia email: nchorfi@ksu.edu.sa |
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Mohamed Jleli Department of Mathematics College of Science, King Saud University P.O. Box 2455, Riyadh 11451, Saudi Arabia email: jleli@ksu.edu.sa |
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