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

Hao Li; Xiangxiong Zhang

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arXiv · 1902.00945

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

Hao Li·Xiangxiong Zhang

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Abstract

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

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BibTeX RIS

Hao Li, Xiangxiong Zhang. 2019-10-22. Superconvergence of $C^0$-$Q^k$ finite element method for elliptic equations with approximated coefficients. https://arxiv.org/abs/1902.00945

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