New locally conservative finite element methods on a rectangular mesh

Youngmok Jeon, Eun-Jae Park

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A new family of locally conservative, finite element methods for a rectangular mesh is introduced to solve second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Quadratic and cubic elements are analyzed and optimal order error estimates measured in the energy norm are provided for elliptic equations. Next, this approach is exploited to approximate Stokes equations. Numerical results are presented for various examples including the lid driven-cavity problem.

Original languageEnglish
Pages (from-to)97-119
Number of pages23
JournalNumerische Mathematik
Volume123
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

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Lid-driven Cavity
Second Order Elliptic Equations
Continuity Equation
Stokes Equations
Elliptic Equations
Error Estimates
Finite Element Method
Mesh
Fluxes
Norm
Finite element method
Numerical Results
Energy
Family

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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New locally conservative finite element methods on a rectangular mesh. / Jeon, Youngmok; Park, Eun-Jae.

In: Numerische Mathematik, Vol. 123, No. 1, 01.01.2013, p. 97-119.

Research output: Contribution to journalArticle

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