A Bi–Hyperbolic Finite Volume Method on Quadrilateral Meshes

H. J. Schroll; F. Svensson

doi:10.1007/s10915-004-4927-9

A Bi–Hyperbolic Finite Volume Method on Quadrilateral Meshes

Journal of Scientific Computing ◽

10.1007/s10915-004-4927-9 ◽

2006 ◽

Vol 26 (2) ◽

pp. 237-260 ◽

Cited By ~ 7

Author(s):

H. J. Schroll ◽

F. Svensson

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Quadrilateral Meshes ◽

Volume Method

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A finite volume method for Stokes problems on quadrilateral meshes

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2018.10.044 ◽

2019 ◽

Vol 77 (4) ◽

pp. 1091-1106 ◽

Cited By ~ 2

Author(s):

Tie Zhang ◽

Zheng Li

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Quadrilateral Meshes ◽

Stokes Problems ◽

Volume Method

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A finite volume method on distorted quadrilateral meshes for discretization of the energy equation's conduction term

Heat Transfer-Asian Research ◽

10.1002/htj.20375 ◽

2011 ◽

Vol 42 (2) ◽

pp. 163-184

Author(s):

Shintaro Murakami ◽

Yutaka Asako

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Quadrilateral Meshes ◽

Volume Method

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An upwind finite volume method on non-orthogonal quadrilateral meshes for the convection diffusion equation in porous media

Applicable Analysis ◽

10.1080/00036811.2015.1064520 ◽

2015 ◽

Vol 95 (10) ◽

pp. 2203-2223 ◽

Cited By ~ 1

Author(s):

Saúl E. Buitrago Boret ◽

Giselle G. Sosa Jones ◽

Oswaldo J. Jiménez P.

Keyword(s):

Porous Media ◽

Diffusion Equation ◽

Finite Volume Method ◽

Finite Volume ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Quadrilateral Meshes ◽

Volume Method

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Comparative Study on Triangular and Quadrilateral Meshes by a Finite-Volume Method with a Central Difference Scheme

Numerical Heat Transfer Part B Fundamentals ◽

10.1080/10407790.2012.709416 ◽

2012 ◽

Vol 62 (4) ◽

pp. 243-263 ◽

Cited By ~ 8

Author(s):

Guojun Yu ◽

Bo Yu ◽

Shuyu Sun ◽

Wen-Quan Tao

Keyword(s):

Comparative Study ◽

Difference Scheme ◽

Finite Volume Method ◽

Finite Volume ◽

Central Difference ◽

Central Difference Scheme ◽

Quadrilateral Meshes ◽

Volume Method

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A Finite Volume Method on Distorted Quadrilateral Meshes for Discretization of Energy Equation's Conduction Term(Thermal Engineering)

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.76.772_2178 ◽

2010 ◽

Vol 76 (772) ◽

pp. 2178-2187 ◽

Cited By ~ 1

Author(s):

Shintaro MURAKAMI ◽

Yutaka ASAKO

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Thermal Engineering ◽

Quadrilateral Meshes ◽

Volume Method

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Simulation of impacts on elastic–viscoplastic solids with the flux-difference splitting finite volume method applied to non-uniform quadrilateral meshes

Advanced Modeling and Simulation in Engineering Sciences ◽

10.1186/s40323-018-0101-z ◽

2018 ◽

Vol 5 (1) ◽

Cited By ~ 1

Author(s):

Thomas Heuzé

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Quadrilateral Meshes ◽

Volume Method ◽

Viscoplastic Solids ◽

Flux Difference

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The hybrid Wilson finite volume method for elliptic problems on quadrilateral meshes

Advances in Computational Mathematics ◽

10.1007/s10444-018-9623-7 ◽

2018 ◽

Vol 45 (1) ◽

pp. 429-452

Author(s):

Yuanyuan Zhang ◽

Min Yang ◽

Chuanjun Chen

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Elliptic Problems ◽

Quadrilateral Meshes ◽

Volume Method

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Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2013.m401 ◽

2015 ◽

Vol 7 (4) ◽

pp. 454-471

Author(s):

Yanli Chen ◽

Yonghai Li

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Elliptic Equations ◽

Stiffness Matrix ◽

Finite Volume Methods ◽

Matrix Analysis ◽

Quadrilateral Meshes ◽

Analysis Technique ◽

The Stability ◽

Volume Method

AbstractIn this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal convergence rate in H1 norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.

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