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

V. O. Pirogov, M. V. Urev

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: 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.

UDC: 519.632

Received: 16.06.2006