phys2dyn.tex

\subsubsection{Mapping algorithm} [Paul: we are just using low-order map? would it be easy to switch to higher-order?] To build the non-monotone ``first guess'' map from the finite volume physics grid to the finite element dynamics grid, a continuous polynomial reconstruction of degree $n_c-1$ (and order $n_c$) is built that exactly interpolates the volume averaged values in each physics grid element.  For the monotone ``first guess'' map, a second-order bilinear reconstruction is instead employed that interpolates the density field at the center of each finite volume.  In each case the reconstruction is then sampled at each of the Gauss-Lobotto-Legendre nodes of the dynamics grid.