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 - <p style="text-align: justify;">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.</p>