Geodesic
A~scheme of a~finite element method for boundary value problems with non-coordinated degeneration of input data
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 313-324

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We construct a scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data and singularity of solution. The rate of convergence of an approximate solution of the proposed finite element method to the exact $R_{\nu}$-generalized solution in the weight set $W^1_{2,\nu^*+\beta/2+1}(\Omega,\delta)$ is investigated, the estimation of finite element approximations is established. 
@article{SJVM_2009_12_3_a6,
     author = {V. A. Rukavishnikov and E. V. Kuznetsova},
     title = {A~scheme of a~finite element method for boundary value problems with non-coordinated degeneration of input data},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {313--324},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2009_12_3_a6/}
}
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V. A. Rukavishnikov; E. V. Kuznetsova. A~scheme of a~finite element method for boundary value problems with non-coordinated degeneration of input data. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 313-324. http://geodesic.mathdoc.fr/item/SJVM_2009_12_3_a6/