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A finite element method for a noncoercive elliptic problem with Neumann boundary conditions
Author(s) -
Kavaliou Klim,
Tobiska Lutz
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210324
Subject(s) - discretization , neumann boundary condition , mathematics , finite element method , norm (philosophy) , boundary (topology) , boundary value problem , mathematical analysis , physics , thermodynamics , law , political science
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 H 1 ‐norm are based on a discrete stability result. Numerical results confirm the theoretical predictions. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)