  The discontinuous Galerkin (DG) finite element method is conservative, lends
itself well to parallelization, and is high-order accurate due to its close
affinity with the theory of quadrature and orthogonal polynomials. When applied
with an orthogonal discretization (\textit{i.e.} a rectilinear grid) the DG
method may be efficiently implemented on a GPU in just a few lines of
high-level language such as Python. This work demonstrates such an
implementation by writing the DG semi-discrete equation in a tensor-product
form and then computing the products using open source GPU libraries. The
results are illustrated by simulating a problem in plasma physics, namely an
instability in the magnetized Vlasov-Poisson system. Further, as DG is closely
related to spectral methods through its orthogonal basis it is possible to
calculate a transformation to an alternative set of global eigenfunctions for
purposes of analysis or to perform additional operations. This transformation
is also posed as a tensor product and may be GPU-accelerated. In this work a
Fourier series is computed for example (although this does not beat discrete
Fourier transform), and is used to solve the Poisson part of the Vlasov-Poisson
system to $\mathcal{O}(\Delta x^{n+1/2})$-accuracy.
