Implicit–explicit multistep characteristic finite element methods for nonlinear convection–diffusion equations

Abstract

AbstractImplicit–explicit multistep characteristic methods are given for convection‐dominated diffusion equations. Multistep difference along characteristics of the one‐order hyperbolic part of the equation is used for discretization in time, and finite element method is used to discrete the space variables. The resulting schemes are consistent, stable and very efficient. Optimal‐rate of convergence is proved. Also, a note is given for a paper published earlier© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007