Approximation of the singularity coefficients of an elliptic equation by mortar spectral element method

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