Geodesic
Solution to first boundary-value problem for weakly degenerating elliptic equation using finite-element method
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 7 (2007) no. 3, pp. 73-85 
V. O. Pirogov; M. V. Urev. Solution to first boundary-value problem for weakly degenerating elliptic equation using finite-element method. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 7 (2007) no. 3, pp. 73-85. http://geodesic.mathdoc.fr/item/VNGU_2007_7_3_a4/
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     title = {Solution to first boundary-value problem for weakly degenerating elliptic equation using finite-element method},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with numerical solution to first boundary-value problem for degenerate 2D elliptic equation using finite-element method. Degeneration of the operator on a part of the boundary requires using weighted functional spaces to analyze variational statement, build difference scheme and prove convergence. We prove that for finite-element method with piece-wise linear elements convergence rate is not worse than in the case of non-degenerating equation. In the last section we demonstrate numerical example to confirm convergence rate.

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