Abstract
L-infinity-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. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 24: 1501-1516, 2008