# Weighted norm least squares finite element method for Poisson equation in a polyhedral domain

Seong Hee Jeong, Eunjung Lee

Research output: Contribution to journalArticle

### Abstract

This paper concerns Poisson equation in a polyhedral domain with corners and edges. We apply the least-squares finite element method to the reformulated first-order system of Poisson equation. To overcome the difficulties from boundary singularities, a weighted-norm technique is used to define the least-squares functional. The method prevents the loss of global accuracy. Numerical simulations are given to demonstrate the theoretical estimates.

Original language English 35-49 15 Journal of Computational and Applied Mathematics 299 https://doi.org/10.1016/j.cam.2015.10.011 Published - 2016 Jun

### Fingerprint

Least-squares Finite Element Method
Weighted Norm
Poisson equation
Poisson's equation
Boundary Singularities
Finite element method
First-order System
Least Squares
Numerical Simulation
Computer simulation
Estimate
Demonstrate

### All Science Journal Classification (ASJC) codes

• Computational Mathematics
• Applied Mathematics

### Cite this

@article{190e4f3ef5314945b8de9d9face4a998,
title = "Weighted norm least squares finite element method for Poisson equation in a polyhedral domain",
abstract = "This paper concerns Poisson equation in a polyhedral domain with corners and edges. We apply the least-squares finite element method to the reformulated first-order system of Poisson equation. To overcome the difficulties from boundary singularities, a weighted-norm technique is used to define the least-squares functional. The method prevents the loss of global accuracy. Numerical simulations are given to demonstrate the theoretical estimates.",
author = "Jeong, {Seong Hee} and Eunjung Lee",
year = "2016",
month = "6",
doi = "10.1016/j.cam.2015.10.011",
language = "English",
volume = "299",
pages = "35--49",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",

}

In: Journal of Computational and Applied Mathematics, Vol. 299, 06.2016, p. 35-49.

Research output: Contribution to journalArticle

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T1 - Weighted norm least squares finite element method for Poisson equation in a polyhedral domain

AU - Jeong, Seong Hee

AU - Lee, Eunjung

PY - 2016/6

Y1 - 2016/6

N2 - This paper concerns Poisson equation in a polyhedral domain with corners and edges. We apply the least-squares finite element method to the reformulated first-order system of Poisson equation. To overcome the difficulties from boundary singularities, a weighted-norm technique is used to define the least-squares functional. The method prevents the loss of global accuracy. Numerical simulations are given to demonstrate the theoretical estimates.

AB - This paper concerns Poisson equation in a polyhedral domain with corners and edges. We apply the least-squares finite element method to the reformulated first-order system of Poisson equation. To overcome the difficulties from boundary singularities, a weighted-norm technique is used to define the least-squares functional. The method prevents the loss of global accuracy. Numerical simulations are given to demonstrate the theoretical estimates.

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DO - 10.1016/j.cam.2015.10.011

M3 - Article

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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