TY - JOUR
T1 - Recent Advances on Explicit Variational Multiscale a Posteriori Error Estimation for Systems
AU - G. Hauke, D. Irisarri & F. Lizarraga
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 372
EP - 384
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/532.html
KW - A posteriori error estimation, stabilized methods.
AB - <p style="text-align: justify;">In 1995 the genesis of stabilized methods was established by Professor Hughes from
the standpoint of the variational multiscale theory (VMS). By splitting the solution into resolved
and unresolved scales, it was unveiled that stabilized methods take into account an approximation
of the unresolved scales or error into the finite element solution. In this work, the VMS theory
is exploited to formulate an explicit a-posteriori error estimator, consistent with the assumptions
inherent to stabilized methods.The proposed technology, which is especially suited for fluid flow
problems, is very economical and can be implemented in standard finite element codes. It has
been shown that, in practice, the method is robust uniformly from the diffusive to the hyperbolic
limit.The success of the method can be explained by the fact that in stabilized methods the
element local problems for the fine-scale Green&#39;s function capture most of the error and the error
intrinsic time-scales are an approximation to the solution of the dual problem. Applications to
the Euler and linear elasticity equations are shown.</p>