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

@article{Pany2021NegativeNE,
  title={Negative norm estimates and superconvergence results in Galerkin method for strongly nonlinear parabolic problems},
  author={Ambit Kumar Pany and Morrakot Khebchareon and Amiya Kumar Pani},
  journal={Comput. Math. Appl.},
  year={2021},
  volume={99},
  pages={26-36}
}
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 ≥ 1 are used, which improve upon earlier results of Axelsson [Numer. Math. 28 (1977), pp. 1-14] requiring for 2d r ≥ 2 and for 3d r ≥ 3. Based on quasi-projection technique… Expand

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