$L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media
Year: 2005
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-933
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 3 : pp. 301–328
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: nonFickian flow mixed finite element methods the mixed Ritz-Volterra projection Green's functions error estimates and superconvergence.