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

The 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.