Adaptive method of lines for magnetohydrodynamic pde models

Many interesting phenomena in plasma fluid dynamics can be described within the framework of magneto-hydrodynamics (MHD). Numerical studies in plasma flows frequently involve simulations with highly varying spatial and temporal scales. As a consequence, numerical methods on uniform grids may be inefficient to use, since a very large number of grid points is needed to resolve the spatial structures, such as shocks, contact discontinuities, shear layers, or current sheets. For the efficient study of these phenomena, we require adaptive grid methods which automatically track and spatially resolve one or more of these structures.