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 languageEnglish
Pages (from-to)35-49
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume299
DOIs
Publication statusPublished - 2016 Jun 1

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

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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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Weighted norm least squares finite element method for Poisson equation in a polyhedral domain. / Jeong, Seong Hee; Lee, Eunjung.

In: Journal of Computational and Applied Mathematics, Vol. 299, 01.06.2016, p. 35-49.

Research output: Contribution to journalArticle

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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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