Bremen 2017 – scientific programme
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P: Fachverband Plasmaphysik
P 15: Helmholtz Graduate School II
P 15.13: Poster
Tuesday, March 14, 2017, 16:30–18:30, HS Foyer
An aligned discontinuous Galerkin method for a non-coercive elliptic operator — •Benedict Dingfelder1, Florian Hindenlang1, 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 (FE). 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 | ⎞ ⎠ | = ω2 φ in Ω (1) |
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 (DG) method with locally aligned cells and basis is presented which improves the numerical accuracy by roughly four digits in comparison to existing methods with the same computational complexity. The results can be used in more complex applications.