TY - JOUR
T1 - $L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 301
EP - 328
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/933.html
KW - nonFickian flow, mixed finite element methods, the mixed Ritz-Volterra projection, Green's functions, error estimates and superconvergence.
AB - <p style="text-align: justify;">On the basis of the estimates for the regularized Green&#39;s
functions with memory terms, optimal order $L^∞$-error estimates
are established for the nonFickian flow of fluid in porous media by
means of a mixed Ritz-Volterra projection. Moreover, local $L^∞$-superconvergence estimates for the velocity along the Gauss
lines and for the pressure at the Gauss points are derived for the mixed
finite element method, and global $L^∞$-superconvergence estimates
for the velocity and the pressure are also investigated by virtue of an
interpolation post-processing technique. Meanwhile, some useful
a-posteriori error estimators are presented for this mixed finite
element method.</p>