  In this work, we propose and develop an arbitrary-order adaptive
discontinuous Petrov-Galerkin (DPG) method for the nonlinear Grad-Shafranov
equation. An ultraweak formulation of the DPG scheme for the equation is given
based on a minimal residual method. The DPG scheme has the advantage of
providing more accurate gradients compared to conventional finite element
methods, which is desired for numerical solutions to the Grad-Shafranov
equation. The numerical scheme is augmented with an adaptive mesh refinement
approach, and a criterion based on the residual norm in the minimal residual
method is developed to achieve dynamic refinement. Nonlinear solvers for the
resulting system are explored and a Picard iteration with Anderson acceleration
is found to be efficient to solve the system. Finally, the proposed algorithm
is implemented in parallel on MFEM using a domain-decomposition approach, and
our implementation is general, supporting arbitrary order of accuracy and
general meshes. Numerical results are presented to demonstrate the efficiency
and accuracy of the proposed algorithm.

Numerical Analysis;Numerical Analysis