Superconvergence of the galerkin approximation of a quasilinear parabolic equation in a single space variable

The asymptotic expansion of the Galerkin solution of a parabolic equation by means of a sequence of elliptic projections that was introduced by Douglas, Dupont, and Wheeder is carried out for a quasilinear equation. This quaxi-projection can be applied to establish knot superconvergence in the case of a single space variable. In addition, an optimal order error estimate in L ^∞ (L ^∞) is derived for a single space variable.