Hannover 2016 – wissenschaftliches Programm
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P: Fachverband Plasmaphysik
P 5: Poster Session- Helmholtz Graduate School for Plasma Physics
P 5.28: Poster
Montag, 29. Februar 2016, 16:30–19:00, Empore Lichthof
A discontinuous Galerkin method for the approximation of eigenvalues of a non coercive elliptic operator — •Benedict Dingfelder1, Ralf Kleiber2, Axel Könies2, and Eric Sonnendrücker1 — 1Max-Planck-Institut für Plasmaphysik, Garching, Deutschland — 2Max-Planck-Institut für Plasmaphysik, Greifswald, Deutschland
Due to the anisotropy introduced by the magnetic field, the equations of ideal MHD show poor convergence properties if they are straight-forwardly discretized by finite elements. In their simplest form, they collapse to a heterogeneous anisotropic diffusion equation with a semidefinite diffusion tensor. The form we consider is given by -∇·( b b^⊤·∇φ) = ω^2 φ in Ω for the two-dimensional periodic domain Ω and direction of the magnetic field b. Despite of its simplicity, the equation reproduces the relevant poor convergence behaviour. A discontinuous Galerkin method with partially aligned cells and a perpendicularly aligned basis is presented which improves the numerical accuracy by roughly two digits in comparison to existing methods with the same computational complexity. The results can be used in more complex applications.