Geodesic
The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 3, pp. 201-228 
A. Yu. Bespalov; V. A. Rukavishnikov. The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 3, pp. 201-228. http://geodesic.mathdoc.fr/item/SJVM_2001_4_3_a0/
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     title = {The use of singular functions in the $h$-$p$ version of the finite element method for a {Dirichlet} problem with degeneration of the input data},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to a Dirichlet problem for a second-order non-self-adjoint elliptic equation with a strong singularity of the solution caused by a coordinated degeneration of input data at boundary points of a two-dimensional domain. The h-p version of the finite element method is used to approximate this problem. We introduce a finite element space with a singular basis that depends on the space to which the solution to the problem belongs. An exponential convergence rate in the norm of a weighted Sobolev space is proved.

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