In this paper,we analyze and provide numerical experiments 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.