TY - JOUR
T1 - A Modified Polynomial Preserving Recovery and Its Applications to a Posteriori Error Estimates
AU - Haijun Wu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 53
EP - 78
PY - 2010
DA - 2010/03
SN - 3
DO - http://doi.org/10.4208/nmtma.2009.m9006
UR - https://global-sci.org/intro/article_detail/nmtma/5989.html
KW - Adaptive finite element method, superconvergence, gradient recovery, modified PPR
AB - <p style="text-align: justify;">A modified polynomial preserving gradient recovery technique is
proposed. Unlike the polynomial preserving gradient recovery
technique, the gradient recovered with the modified polynomial
preserving recovery (MPPR) is constructed element-wise, and it is
discontinuous across the interior edges. One advantage of the MPPR
technique is that the implementation is easier when adaptive meshes
are involved. Superconvergence results of the gradient recovered
with MPPR are proved for finite element methods for elliptic
boundary problems and eigenvalue problems under adaptive meshes. The
MPPR is applied to adaptive finite element methods to construct
asymptotic exact a posteriori error estimates. Numerical tests are
provided to examine the theoretical results and the effectiveness of
the adaptive finite element algorithms.</p>