An Analysis of Some Galerkin Schemes for the Solution of Nonlinear Time-Dependent Problems

A priori error estimates are derived for several Galerkin procedures. For a nonlinear parabolic initial-boundary value problem, optimal rate $L^2 $-error estimates are derived for the forward and central difference Laplace modified Galerkin methods and the forward and central difference Laplace modified alternating direction Galerkin methods. For a nonlinear second order hyperbolic initial-boundary value problem, optimal rate $L^2 $-error estimates are derived for the Laplace modified Galerkin method and the Laplace modified alternating direction Galerkin method.