New locally conservative finite element methods on a rectangular mesh

Youngmok Jeon; Eun Jae Park

doi:10.1007/s00211-012-0477-5

New locally conservative finite element methods on a rectangular mesh

Youngmok Jeon, Eun Jae Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

12 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 language	English
Pages (from-to)	97-119
Number of pages	23
Journal	Numerische Mathematik
Volume	123
Issue number	1
DOIs	https://doi.org/10.1007/s00211-012-0477-5
Publication status	Published - 2013 Jan

Bibliographical note

Funding Information:
Research of Y. Jeon was supported by NRF 2010-0021683, and E.-J. Park was supported in part by the WCU program through NRF R31-10049.

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1007/s00211-012-0477-5

Cite this

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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.",

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N2 - 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.

AB - 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.

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New locally conservative finite element methods on a rectangular mesh

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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