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

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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. 
@article{VNGU_2007_7_3_a4,
     author = {V. O. Pirogov and M. V. Urev},
     title = {Solution to first boundary-value problem for weakly degenerating elliptic equation using finite-element method},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {73--85},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2007_7_3_a4/}
}
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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/