Negative norm estimates and superconvergence results in Galerkin method for strongly nonlinear parabolic problems

The conforming finite element Galerkin method is applied to discretise in the spatial direction for a class of strongly nonlinear parabolic problems. Using elliptic projection associated linearised stationary problem with Gronwall type result, optimal error estimates are derived, when piecewise polynomials degree r≥1 used, which improve upon earlier results Axelsson ((1977) [3]) requiring 2d r≥2 and 3d r≥3. Based on quasi-projection technique introduced by Douglas et al. ((1978) [11]), superconvergence result between approximation through established semidiscrete scheme. Further, priori Sobolev spaces negative index derived. Moreover, single space variable, nodal true solution established.