PAMM
Volume 12, Issue 1 pp. 671-672
Section 18
Free Access

A finite element method for a noncoercive elliptic problem with Neumann boundary conditions

Klim Kavaliou, 

Corresponding Author

Klim Kavaliou

Institute of Analysis and Computational Mathematics, Faculty of Mathematics, Otto-von-Guericke University Magdeburg, PF 4120, D-39106 Magdeburg, Germany

Klim Kavaliou, phone +49 391 67 12633 fax +49 391 67 18073

Lutz Tobiska, phone +49 391 67 18650 fax +49 391 67 18073

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Lutz Tobiska, 

Corresponding Author

Lutz Tobiska

Institute of Analysis and Computational Mathematics, Faculty of Mathematics, Otto-von-Guericke University Magdeburg, PF 4120, D-39106 Magdeburg, Germany

Klim Kavaliou, phone +49 391 67 12633 fax +49 391 67 18073

Lutz Tobiska, phone +49 391 67 18650 fax +49 391 67 18073

Search for more papers by this author
First published: 03 December 2012
https://doi.org/10.1002/pamm.201210324

Abstract

We consider a noncoercive convection-diffusion problem with Neumann boundary conditions appearing in modeling of magnetic fluid seals. The associated operator has a non-trivial one-dimensional kernel spanned by a positive function. A discretization is proposed preserving these properties. Optimal error estimates in the H1-norm are based on a discrete stability result. Numerical results confirm the theoretical predictions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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