A generalization of the vertex-centered finite volume scheme to arbitrary high order

Andreas Vogel; Jinchao Xu; Gabriel Wittum

doi:10.1007/s00791-010-0139-z

A generalization of the vertex-centered finite volume scheme to arbitrary high order

Andreas Vogel, Jinchao Xu, Gabriel Wittum

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

17 Scopus citations

Abstract

A higher order finite volume method for elliptic problems is proposed for arbitrary order p ∈ ℕ. Piecewise polynomial basis functions are used as trial functions while the control volumes are constructed by a vertex-centered technique. The discretization is tested on numerical examples utilizing triangles and quadrilaterals in 2D. In these tests the optimal error is achieved in the H 1-norm. The error in the L 2-norm is one order below optimal for even polynomial degrees and optimal for odd degrees. © 2010 Springer-Verlag.

Original language	English (US)
Pages (from-to)	221-228
Number of pages	8
Journal	Computing and Visualization in Science
Volume	13
Issue number	5
DOIs	https://doi.org/10.1007/s00791-010-0139-z
State	Published - Jun 1 2010
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Theoretical Computer Science
Software
Computer Vision and Pattern Recognition
General Engineering

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AU - Xu, Jinchao

AU - Wittum, Gabriel

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PY - 2010/6/1

Y1 - 2010/6/1

N2 - A higher order finite volume method for elliptic problems is proposed for arbitrary order p ∈ ℕ. Piecewise polynomial basis functions are used as trial functions while the control volumes are constructed by a vertex-centered technique. The discretization is tested on numerical examples utilizing triangles and quadrilaterals in 2D. In these tests the optimal error is achieved in the H 1-norm. The error in the L 2-norm is one order below optimal for even polynomial degrees and optimal for odd degrees. © 2010 Springer-Verlag.

AB - A higher order finite volume method for elliptic problems is proposed for arbitrary order p ∈ ℕ. Piecewise polynomial basis functions are used as trial functions while the control volumes are constructed by a vertex-centered technique. The discretization is tested on numerical examples utilizing triangles and quadrilaterals in 2D. In these tests the optimal error is achieved in the H 1-norm. The error in the L 2-norm is one order below optimal for even polynomial degrees and optimal for odd degrees. © 2010 Springer-Verlag.

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JO - Computing and Visualization in Science

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ER -

A generalization of the vertex-centered finite volume scheme to arbitrary high order

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