  An overview of the algorithm and a sampling of plasma applications of the
implicit, adaptive high order finite (spectral) element modeling framework,
HiFi, is presented. The distinguishing capabilities of the HiFi code include
adaptive spectral element spatial representation with flexible geometry, highly
parallelizable implicit time advance, and general flux-source form of the
partial differential equations and boundary conditions that can be implemented
in its framework. Early algorithm development and extensive verification
studies of the two-dimensional version of the code, known as SEL, have been
previously described [A.H. Glasser & X.Z. Tang, Comp. Phys. Comm., 164 (2004);
V.S. Lukin, Ph.D. thesis, Princeton University (2008)]. Here, substantial
algorithmic improvements and extensions are presented together with examples of
two- and three- dimensional applications of the HiFi framework. These include a
Cartesian two-dimensional incompressible magnetohydrodynamic simulation of low
dissipation magnetic reconnection in a large system, a two-dimensional
axisymmetric simulation of self-similar compression of a magnetic plasma
confinement configuration, and a three-dimensional Hall MHD simulation of
spheromak tilting and relaxation. Some planned efforts to further improve and
expand the capabilities of the HiFi modeling framework are discussed.
