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 of the associated linearised stationary problem with Gronwall type result, optimal error estimates are derived, when piecewise polynomials of degree $r\ge 1$ are used, which improve upon earlier results of Axelsson ((1977) [3]) requiring for 2d $r\ge 2$ and for 3d $r\ge 3$. Based on quasi-projection technique introduced by Douglas et al. ((1978) [11]), superconvergence result for the error between Galerkin approximation and approximation through quasi-projection is established for the semidiscrete Galerkin scheme. Further, a priori error estimates in Sobolev spaces of negative index are derived. Moreover, in a single space variable, nodal superconvergence results between the true solution and Galerkin approximation are established.

对于一类强非线性抛物线问题，采用符合有限元Galerkin方法在空间方向上离散。使用具有 Gronwall 类型结果的相关线性化平稳问题的椭圆投影，当阶数分段多项式$r\ge 1$ 使用，它改进了 Axelsson ((1977) [3]) 需要 2d 的早期结果 $r\ge 2$ 和 3d $r\ge 3$. 基于 Douglas 等人介绍的准投影技术。((1978) [11])，半离散伽辽金方案建立了伽辽金近似与准投影近似误差的超收敛结果。进一步推导了负指数Sobolev空间中的先验误差估计。此外，在单个空间变量中，建立了真解与伽辽金近似之间的节点超收敛结果。