  The Galileon theory is a prototypical effective field theory that
incorporates the Vainshtein screening mechanism--a feature that arises in some
extensions of General Relativity, such as massive gravity. The Vainshtein
effect requires that the theory contain higher order derivative interactions,
which results in Galileons, and theories like them, failing to be technically
well-posed. While this is not a fundamental issue when the theory is correctly
treated as an effective field theory, it nevertheless poses significant
practical problems when numerically simulating this model. These problems can
be tamed using a number of different approaches: introducing an active low-pass
filter and/or constructing a UV completion at the level of the equations of
motion, which controls the high momentum modes. These methods have been tested
on cubic Galileon interactions, and have been shown to reproduce the correct
low-energy behavior. Here we show how the numerical UV-completion method can be
applied to quartic Galileon interactions, and present the first simulations of
the quartic Galileon model using this technique. We demonstrate that our
approach can probe physics in the regime of the effective field theory in which
the quartic term dominates, while successfully reproducing the known results
for cubic interactions.
