Generalized Time Integration Schemes for Space-Time Moving Finite Elements
Numerical Analysis
2013-10-30 v1
Abstract
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.
Cite
@article{arxiv.1310.7611,
title = {Generalized Time Integration Schemes for Space-Time Moving Finite Elements},
author = {Randolph E. Bank and Maximilian S. Metti},
journal= {arXiv preprint arXiv:1310.7611},
year = {2013}
}