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Volume 37, Issue 3
A Diagonally-Implicit Time Integration Scheme for Space-Time Moving Finite Elements

Randolph E. Bank & Maximilian S. Metti

DOI: 10.4208/jcm.1805-m2017-0102

J. Comp. Math., 37 (2019), pp. 360-383.

Published online: 2018-09

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

TR-BDF2, Moving finite elements, Method of characteristics, Convection-dominated, Moving mesh methods, Error analysis.

  • AMS Subject Headings

65M55, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rbank@ucsd.edu (Randolph E. Bank)

maxx@adtile.me (Maximilian S. Metti)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-360, author = {Bank , Randolph E. and Metti , Maximilian S.}, title = {A Diagonally-Implicit Time Integration Scheme for Space-Time Moving Finite Elements}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1805-m2017-0102}, url = {http://global-sci.org/intro/article_detail/jcm/12728.html} }
TY - JOUR T1 - A Diagonally-Implicit Time Integration Scheme for Space-Time Moving Finite Elements AU - Bank , Randolph E. AU - Metti , Maximilian S. JO - Journal of Computational Mathematics VL - 3 SP - 360 EP - 383 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1805-m2017-0102 UR - https://global-sci.org/intro/article_detail/jcm/12728.html KW - TR-BDF2, Moving finite elements, Method of characteristics, Convection-dominated, Moving mesh methods, Error analysis. AB -

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.

Bank , Randolph E. and Metti , Maximilian S.. (2018). A Diagonally-Implicit Time Integration Scheme for Space-Time Moving Finite Elements. Journal of Computational Mathematics. 37 (3). 360-383. doi:10.4208/jcm.1805-m2017-0102
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