Two-Level Discrete-Time Galerkin Approximations for Second Order Nonlinear Parabolic Partial Differential Equations

Galerkin methods for nonlinear parabolic problems are studied. For suitable space domains in R³, two-level discrete-time methods are proposed which are shown to yield optimal order of approximation for a more general class of problem than has been analyzed heretofore. An induction argument is used to treat nonlinear capacity terms. One method studied yields second order convergence in time while requiring the solution of a linear algebraic system only once per time step.