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A Finite Element Method for a Noncoercive Elliptic Problem with Neumann Boundary Conditions

Klim Kavaliou and Lutz Tobiska

Abstract

We apply a combined finite-element finite-volume method on a noncoercive elliptic boundary value problem. The proposed method is based on triangulations of weakly acute type and a secondary circumcentric subdivision. The properties of the continuous problem, that the kernel is one-dimensional and spanned by a positive function, are preserved in the discrete case. A priori error estimates of first order in the H¹-norm are shown for sufficiently small mesh sizes. Numerical test examples confirm the theoretical predictions.

Received: 2011-12-15
Revised: 2012-03-16
Accepted: 2012-03-21
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus