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

Seong Hee Jeong; Eunjung Lee

doi:10.1016/j.cam.2015.10.011

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

Seong Hee Jeong, Eunjung Lee

Department of Computational Science and Engineering

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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
Pages (from-to)	35-49
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	299
DOIs	https://doi.org/10.1016/j.cam.2015.10.011
Publication status	Published - 2016 Jun

Bibliographical note

Funding Information:
This work was supported by NRF grant 2015 R1A5A1009350 .

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2015.10.011

Cite this

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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.",

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

Abstract

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