  In this paper, we analyze and provide numerical illustrations for a moving
finite element method applied to convection-dominated, time-dependent partial
differential equations. We follow a method of lines approach and utilize an
underlying tensor-product finite element space that permits the mesh to evolve
continuously in time and undergo discontinuous reconfigurations at discrete
time steps. We employ the TR-BDF2 method as the time integrator for piecewise
quadratic tensor-product spaces, and provide an almost symmetric error estimate
for the procedure. Our numerical results validate the efficacy of these moving
finite elements.

Numerical Analysis