# Lp error estimates and superconvergence for finite element approximations for nonlinear parabolic problems

• LI, QIAN (Department of Mathematics Shandong Normal University) ;
• DU, HONGWEI (College of Business Administration Midwetern State University)
• Published : 2000.06.30

#### Abstract

In this paper we consider finite element mathods for nonlinear parabolic problems defined in ${\Omega}{\subset}R^d$ ($d{\leq}4$). A new initial approximation is taken. Optimal order error estimates in $L_p$ for $2{\leq}p{\leq}{\infty}$ are established for arbitrary order finite element. One order superconvergence in $W^{1,p}$ for $2{\leq}q{\leq}{\infty}$ are demonstrated as well.

#### Acknowledgement

Supported by : NSF of China