L ∞ -error estimates for finite element for Galerkin solutions for the Benjamin-Bona-Mahony-Burgers (BBMB) equation are considered. A priori bound and the semidiscrete Galerkin scheme are studied using appropriate projections. For fully discrete Galerkin schemes, we consider the backward Euler method and analyze the corresponding error estimates. For a second order accuracy in time, we propose a three-level backward method.

a b s t r a c tIn this paper, we present a Crank-Nicolson type finite difference scheme to approximate the nonlinear evolutionary Extended Fisher-Kolmogorov (EFK) equation. We prove the existence of the solution by using the well-known Browder fixed-point theorem. The stability of this scheme is established in L ∞ -norm. The uniqueness and convergence of the solution are analyzed. We discuss an iterative algorithm for solving the difference scheme and prove its convergence.

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