A simple third order compact finite element method for 1D BVP

Baiying Dong; Zhilin Li

A simple third order compact finite element method for 1D BVP

Numerical Analysis 2021-08-17 v1 Numerical Analysis

Authors: Baiying Dong , Zhilin Li

Abstract

A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimate, which can be related to the source term. Thus, a simple posterior error analysis or a modified basis functions based on original piecewise linear basis function will lead to a third order accurate solution in the $L^2$ norm, and second order in the $H^1$ or the energy norm. Numerical examples have confirmed our analysis.

Keywords

finite element method mixed finite element methods sturm-liouville operators

Cite

@article{arxiv.2108.06627,
  title  = {A simple third order compact finite element method for 1D BVP},
  author = {Baiying Dong and Zhilin Li},
  journal= {arXiv preprint arXiv:2108.06627},
  year   = {2021}
}

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9 pages

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