@Article{IJNAM-2-301, author = {}, title = {$L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {3}, pages = {301--328}, abstract = {

On the basis of the estimates for the regularized Green'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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/933.html} }