A Nonconforming Characteristic Finite Element Method for Nonlinear Advection-Dominated Diffusion Equation with Memory Term

Abstract

A nonconforming characteristic finite element method is considered for nonlinear convection-dominated diffusion equation with memory term. By the use of some special properties of the finite element interpolation operator, and without Rietz-Volterra projection operator which is an indispensable tool in the convergence analysis of finite element methods for integro-differential evolution equations in the previous literature, the optimal error estimate on L2-norm and the superconvergence result on H 1-norm are obtained. © Springer-Verlag Berlin Heidelberg 2013.