TY - JOUR
T1 - An Adaptive Linear Time Stepping Algorithm for Second-Order Linear Evolution Problems
AU - Junjiang Lai & Jianguo Huang
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 230
EP - 253
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/486.html
KW - A posteriori error analysis, adaptive algorithm, linear finite element, evolution problems.
AB - <p style="text-align: justify;">In this paper, we propose and analyze a linear time stepping finite element method
for abstract second order linear evolution problems. For such methods, we derive optimal order a
posteriori error estimates and sharp a posteriori nodal error estimates using the energy approach
and the duality argument. Based on these estimates, we further design an adaptive time stepping
strategy for the previous discretization in time. Several numerical experiments are provided to
show the reliability and efficiency of the a-posteriori error estimates and to assess the effectiveness
of the proposed adaptive time stepping method.</p>