An adaptive finite element method for magnetohydrodynamics

A finite element discretization for two-dimensional MHD is described. The e lements are triangles with piecewise linear basis functions. The main compu tational difficulty is the accurate calculation of the current. The most ef fective solution is to employ a current-vorticity advection formulation of the equations. Acceptable results can also be obtained with a two-step calc ulation of the current from the vector potential. Mesh operations are descr ibed to reconnect and refine the mesh adaptively in the vicinity of nearly singular currents to improve magnetic flux conservation. Example computatio ns of the coalescence instability, tilt mode, and divertor tokamak equilibr ium, validating and illustrating the method, are presented. The simulations show the formation of current sheets, with the current density increasing exponentially in time. During this increase, the grid of initially similar to 10(4) points adapts to provide resolution comparable to a uniform grid o f up to 1.6 x 10(8) grid points. (C) 1998 Academic Press.