In this work we present a mimetic spectral element discretization for the 2D incompressible
Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass …

In this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD)
equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas …

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in
terms of the solution to a semi-linear elliptic equation known as the Grad–Shafranov …

We propose a high-order adaptive numerical solver for the semilinear elliptic boundary
value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices …

In this work, we propose and develop an arbitrary-order adaptive discontinuous Petrov--
Galerkin (DPG) method for the nonlinear Grad--Shafranov equation. An ultraweak …

We introduce a domain decomposition structure-preserving method based on a hybrid
mimetic spectral element method for three-dimensional linear elasticity problems in …

Existing finite element implementations for the computation of free-boundary axisymmetric
plasma equilibria approximate the unknown poloidal flux function by standard lowest order …

A new method for mimetic interpolation on polygonal meshes is described. This new method
is based on harmonic function interpolation. Explicit formulas for harmonic functions on …

This chapter addresses the topological structure of steady, anisotropic, inhomogeneous
diffusion problems. Differential operators are represented by sparse incidence matrices …

In tokamak plasmas, the current density profile is a strong determiner of both MHD stability
and confinement. The design of active control techniques for this profile relies on control …