Solution to first boundary-value problem for weakly degenerating elliptic equation using finite-element method

This paper deals with numerical solution to first boundary-value problem for degenerate 2D elliptic equation using finite-element method. Degeneration of the operator on a part of the boundary requires using weighted functional spaces to analyze variational statement, build difference scheme and prove convergence. We prove that for finite-element method with piece-wise linear elements convergence rate is not worse than in the case of non-degenerating equation. In the last section we demonstrate numerical example to confirm convergence rate.