TY - JOUR
T1 - Cell Conservative Flux Recovery and a Posteriori Error Estimate of Vertex-Centered Finite Volume Methods
AU - Chen , Long
AU - Wang , Ming
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 705
EP - 727
PY - 2013
DA - 2013/05
SN - 5
DO - http://doi.org/10.4208/aamm.12-m1279
UR - https://global-sci.org/intro/article_detail/aamm/93.html
KW - Finite volume methods, flux recovery, a posteriori error estimates.
AB - <p style="text-align: justify;">A cell conservative flux recovery technique is developed here for vertex-centered
finite volume methods of second order elliptic equations.
It is based on solving a local Neumann problem on each control volume using mixed
finite element methods. The recovered flux is used to
construct a constant free a posteriori error estimator which is proven to be
reliable and efficient. Some numerical tests are presented
to confirm the theoretical results. Our method works for general order finite volume
methods and the recovery-based and residual-based
a posteriori error estimators are the first result on
a posteriori error estimators for high
order finite volume methods.</p>