The finite element method for a boundary value problem with strong singularity

Authors:
V. A. Rukavishnikov;H. I. Rukavishnikova
Affiliations:
Computing Center, Far-Eastern Branch, Russian Academy of Sciences, Jambula Str. 25-260, Khabarovsk 680011, Russia;Computing Center, Far-Eastern Branch, Russian Academy of Sciences, Jambula Str. 25-260, Khabarovsk 680011, Russia
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The existence and uniqueness of the R"@n-generalized solution for the third-boundary-value problem and the non-self-adjoint second-order elliptic equation with strong singularity are established. We construct a finite element method with a basis containing singular functions. The rate of convergence of the approximate solution to the R"@n-generalized solution in the norm of the Sobolev weighted space is established and, finally, results of numerical experiments are presented.