a b s t r a c tThe existence and uniqueness of the R ν -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 ν -generalized solution in the norm of the Sobolev weighted space is established and, finally, results of numerical experiments are presented.

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