H1-second order convergent estimates for non-Fickian models
Applied Numerical Mathematics
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
Journal of Scientific Computing
Computers & Mathematics with Applications
Supraconvergence and supercloseness in Volterra equations
Applied Numerical Mathematics
Journal of Computational Physics
Analysis of mixed finite element methods for fourth-order wave equations
Computers & Mathematics with Applications
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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 L2 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.