On the error estimation of the finite element method for the third boundary value problem with singularity in the space $L_{2,\nu+\gamma}^*$

The paper analyzes the finite element method for the third boundary value problem for non-self-conjugate second order elliptic equation with coordinated degeneration of initial data and with strong singularity of solution. The scheme of the finite element method is constructed on the basis of the definition of $R_{\nu}$-generalized solution to the problem, and the finite element space contains singular power functions. It is established that the rate of convergence of an approximate solution to the exact $R_{\nu}$-generalized solution in the norm of the Lebesgue weight space $L_{2,\nu+\gamma}^*\Omega$ has second order.