Year: 2019
Author: Randolph E. Bank, Maximilian S. Metti
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 3 : pp. 360–383
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1805-m2017-0102
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 3 : pp. 360–383
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: TR-BDF2 Moving finite elements Method of characteristics Convection-dominated Moving mesh methods Error analysis.