  In this paper, we present a new static and time-dependent MagnetoHydroDynamic
(MHD) equilibrium code, TokaMaker, for axisymmetric configurations of
magnetized plasmas, based on the well-known Grad-Shafranov equation. This code
utilizes finite element methods on an unstructured triangular grid to enable
capturing accurate machine geometry and simple mesh generation from
engineering-like descriptions of present and future devices. The new code is
designed for ease of use without sacrificing capability and speed through a
combination of Python, Fortran, and C/C++ components. A detailed description of
the numerical methods of the code, including a novel formulation of the
boundary conditions for free-boundary equilibria, and validation of the
implementation of those methods using both analytic test cases and cross-code
validation is shown. Results show expected convergence across tested polynomial
orders for analytic and cross-code test cases.
