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 - finite element method at the Gauss Lobatto quadrature points still holds if variable coefficients in an elliptic problem are replaced by their piecewise Lagrange interpolant at the Gauss Lobatto points in each rectangular cell. In particular, a fourth order finite difference type scheme can be constructed using - finite element method with 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}
}