Sharp L2 -Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media Academic Article

abstract

• A sharper L2-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz-Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75-84]. Moreover, local L 2 superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points is derived for the mixed finite element method via the Ritz-Volterra projection, and global L2 superconvergence for the velocity and the pressure is also investigated by virtue of an interpolation postprocessing technique. On the basis of the superconvergence estimates, some useful a posteriori error estimators are presented for this mixed finite element method.

authors

• Lin, Yuqing

published proceedings

• SIAM Journal on Numerical Analysis

author list (cited authors)

• Ewing, R. E., Lin., Y., Sun., T., Wang., J., & Zhang, S.

citation count

• 36

complete list of authors

• Ewing, Richard E||Lin., Yanping||Sun., Tong||Wang., Junping||Zhang, Shuhua

publication date

• January 2002

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• 49 Mathematical Sciences
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1137/s0036142900378406

URI

• https://hdl.handle.net/1969.1/180187

start page

• 1538

end page

• 1560

volume

• 40

issue

• 4

URL

• http://dx.doi.org/10.1137/s0036142900378406