We present the first results from a new unstructured mesh three dimensional finite element MHD code which uses dynamic solution-adaptive mesh refinement in a manner similar to our two dimensional finite element MHD code /31/. The problem being considered here is the interaction of the solar wind with the earth's magnetosphere, using a three-dimensional Cartesian approximation. Our results strongly indicate that such adaptive mesh techniques have the ability to resolve structures in the three dimensional MHD flow field that would otherwise be possible only with orders of magnitude greater cost and that are most likely beyond the capability of present supercomputers
