SUPERCONVERGENCE OF FINITE ELEMENT METHODS FOR LINEAR QUASI-PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

• Li, Qian (School of Mathematics Shandong Normal University) ;
• Shen, Wanfang (School of Mathematics Shandong Normal University) ;
• Jian, Jinfeng (School of Mathematics Shandong Normal University)
• Published : 2004.12.25

Abstract

We consider finite element methods applied to a class of quasi parabolic integro-differential equations in $R^d$. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in $W^{1,p}(\Omega)\;and\;L_p(\Omega)$, for $2\;{\leq}p\;<\;{\infty}$.