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Superconvergence of $C^0$-$Q^k$ finite element method for elliptic equations with approximated coefficients

Numerical Analysis 2019-10-24 v2 Numerical Analysis

Abstract

We prove that the superconvergence of C0C^0-QkQ^k finite element method at the Gauss Lobatto quadrature points still holds if variable coefficients in an elliptic problem are replaced by their piecewise QkQ^k Lagrange interpolant at the Gauss Lobatto points in each rectangular cell. In particular, a fourth order finite difference type scheme can be constructed using C0C^0-Q2Q^2 finite element method with Q2Q^2 approximated coefficients.

Keywords

Cite

@article{arxiv.1902.00945,
  title  = {Superconvergence of $C^0$-$Q^k$ finite element method for elliptic equations with approximated coefficients},
  author = {Hao Li and Xiangxiong Zhang},
  journal= {arXiv preprint arXiv:1902.00945},
  year   = {2019}
}