TY - JOUR T1 - A Modified Polynomial Preserving Recovery and Its Applications to a Posteriori Error Estimates 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 -

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.