This article is cited in 4 papers

Convergence of the finite element method for elliptic equations with strong degeneration

M. V. Urev<sup>ab

a</sup> Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrent'ev av., 630090 Novosibirsk
^b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk

Abstract: We consider the questions of numerical solution by the finite element method (FEM) for the first boundary value problem for an elliptic equation with degeneration on a part of the boundary. We pose the weak and strong variational statements in the function spaces with compatible weights that correspond to the problem. Using the method of the multiplicative separation of singularity for the finite element method that utilizes piecewise linear elements, we prove that the convergence of the approximate solutions to the exact solution in the weighted norm is no worse than in the case of an elliptic equation without degeneracy.

Keywords: elliptic equation with degeneracy, weighted Sobolev space, multiplicative separation of singularity, finite element method, convergence.

UDC: 519.632

Received: 10.01.2014

 English version: Journal of Applied and Industrial Mathematics, 2014, 8:3, 411–421

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