Author: Brian S Cornille
Requested Type: Poster
Submitted: 2018-02-28 11:18:41
Co-authors: C.R. Sovinec
University of Wisconsin-Madison
510 Engineering Research Build
Madison, WI 53706
We are investigating the first-order system least-squares (FOSLS) method  as a means to more robust Hall-MHD with the NIMROD code [https://nimrodteam.org]. FOSLS differs from Galerkin element-based methods and leads to stable symmetric algebraic systems at the cost of having to solve larger systems. Formulations that simultaneously solve for magnetic field (B) and current density, including divergence constraints, effectively apply both curl and divergence operators, and the H1 function space is appropriate. Example results from this formulation demonstrate its feasibility. Formulations with B and electric field or with B and vector potential are simpler, but H(curl) conforming finite elements are required. This type of finite element is distinct from continuous H1-conforming finite elements and only provides continuity of the tangential component of a vector field across element boundaries. The degrees of freedom of an H(curl) conforming finite element are related to covariant vector components of the represented field. To evaluate the vector components of such a field from the orthonormal coordinate system of a reference element, an appropriate transformation must be applied. The use of H(curl) and H(div) conforming finite elements was originally pioneered for electromagnetic applications. Due to the Fourier representation of the periodic coordinate in NIMROD, we have adapted previously developed H(curl) basis approximations for our computations. We present the development of the appropriate H(curl) conforming hybrid 2-D finite element and 1-D Fourier spectral series for the NIMROD implementation.
 C. A. Leibs and T. A. Manteuffel, SIAM J. Sci. Comput. 37, S314 (2015).
*Supported by the US DOE CSGF program and by grant DE-FC02-08ER54974.