FINITE VOLUME ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

  • LI, QIAN (Department of Mathematics Shandong Normal University) ;
  • LIU, ZHONGYAN (Department of Mathematics Shandong Normal University)
  • Published : 2002.12.31

Abstract

In this paper, finite volume element methods for nonlinear parabolic problems are proposed and analyzed. Optimal order error estimates in $W^{1,p}$ and $L_p$ are derived for $2{\leq}p{\leq}{\infty}$. In addition, superconvergence for the error between the approximation solution and the generalized elliptic projection of the exact solution (or and the finite element solution) is also obtained.