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

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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.

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 2010

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Software
Modeling and Simulation
Engineering(all)
Computer Vision and Pattern Recognition
Computational Theory and Mathematics

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10.1007/s00791-010-0139-z

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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.",

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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.

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

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