A scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data

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.