A Diagonally-Implicit Time Integration Scheme for Space-Time Moving Finite Elements

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.

Author Details

Randolph E. Bank

Maximilian S. Metti