A Diagonally-Implicit Time Integration Scheme for Space-Time Moving Finite Elements (Journal of Computational Mathematics, 2019)
In this paper, we analyze and provide numerical experiments for a moving finite elementmethod applied to convection-dominated, time-dependent partial differential equations.We follow a method of lines approach and utilize an underlying tensor-productfinite element space that permits the mesh to evolve continuously in time and undergodiscontinuous reconfigurations at discrete time steps. We employ the TR-BDF2 method asthe time integrator for piecewise quadratic tensor-product spaces, and provide an almostsymmetric error estimate for the procedure. Our numerical results validate the efficacy ofthese moving finite elements.