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.
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 H 1 -norm are shown for sufficiently small mesh sizes. Numerical test examples confirm the theoretical predictions.2010 Mathematical subject classification: 65N30; 65N15.
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