When developing numerical algorithms for problems with multiple time-scales, the method of temporal discretization typically receives primary attention. However, spatial discretization errors have a great impact on practical calculations of temporally stiff conditions, where the CFL condition must be exceeded for many of the modes supported by the system. Magnetohydrodynamics calculations for fusion plasmas are particularly sensitive to spatial errors, due to the anisotropy imposed by the magnetic field. Here, we review the benefits and challenges of applying high-order finite elements with respect to the eigenvalues of the time-advance operation, the magnetic divergence constraint, and anisotropies.
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