Geodesic
On the $h$-$p$ version of the finite element method for one-dimensional boundary value problem with singularity of a solution
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 153-170 
V. A. Rukavishnikov; A. Yu. Bespalov. On the $h$-$p$ version of the finite element method for one-dimensional boundary value problem with singularity of a solution. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 153-170. http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper analyzes the $h$-$p$ version of the finite element method for a one-dimensional model boundary value problem with coordinated degeneration of initial data and with strong singularity of a solution. The scheme of the finite element method is constructed on the basis of the definition of $R_\nu$-generalized solution to the problem, and the finite element space contains singular power functions. By using meshes with concentration at a singular point and by constructing the linear degree vector of approximating functions in a special way, a nearly optimal two-sided exponential estimate is obtained for the residual of the finite element method.

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