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The conforming finite element Galerkin method is applied to discretise in thespatial direction for a class of strongly nonlinear parabolic problems. Usingelliptic projection of the associated linearised stationary problem withGronwall type result, optimal error estimates are derived, when piecewisepolynomials of degree $r\geq 1$ are used, which improve upon earlier results ofAxelsson [Numer. Math. 28 (1977), pp. 1-14] requiring for 2d $r\geq 2$ and for3d $r\geq 3.$ Based on quasi-projection technique introduced by Douglas {\it etal.} [Math. Comp.32 (1978),pp. 345-362], superconvergence result for the errorbetween Galerkin approximation and approximation through quasi-projection isestablished for the semidiscrete Galerkin scheme. Further, {\it a priori} errorestimates in Sobolev spaces of negative index are derived. Moreover, in asingle space variable, nodal superconvergence results between the true solutionand Galerkin approximation are established.

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