Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes

Journal of Computational Physics ◽

10.1016/j.jcp.2008.09.031 ◽

2009 ◽

Vol 228 (3) ◽

pp. 703-716 ◽

Author(s):

K. Lipnikov ◽

D. Svyatskiy ◽

Y. Vassilevski

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Polygonal Meshes ◽

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A monotone finite volume method for advection–diffusion equations on unstructured polygonal meshes

Journal of Computational Physics ◽

10.1016/j.jcp.2010.01.035 ◽

2010 ◽

Vol 229 (11) ◽

pp. 4017-4032 ◽

Author(s):

K. Lipnikov ◽

D. Svyatskiy ◽

Y. Vassilevski

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Polygonal Meshes ◽

Advection Diffusion ◽

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A finite volume method based on radial basis functions for two-dimensional nonlinear diffusion equations

Applied Mathematical Modelling ◽

10.1016/j.apm.2005.07.007 ◽

2006 ◽

Vol 30 (10) ◽

pp. 1118-1133 ◽

Author(s):

T.J. Moroney ◽

I.W. Turner

Keyword(s):

Finite Volume Method ◽

Radial Basis Functions ◽

Finite Volume ◽

Nonlinear Diffusion ◽

Basis Functions ◽

Diffusion Equations ◽

Two Dimensional ◽

Nonlinear Diffusion Equations ◽

Radial Basis ◽

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An upwind finite volume method for convection-diffusion equations on rectangular mesh

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2018.09.011 ◽

2019 ◽

Vol 118 ◽

pp. 159-165 ◽

Author(s):

Jiawei Tan

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Convection Diffusion ◽

Rectangular Mesh ◽

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A finite volume method with a modified ENO scheme using a Hermite interpolation to solve advection diffusion equations

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.123 ◽

2001 ◽

Vol 50 (10) ◽

pp. 2339-2371 ◽

Author(s):

A. Balaguer ◽

C. Conde ◽

J. A. López ◽

V. Martínez

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Hermite Interpolation ◽

Diffusion Equations ◽

Advection Diffusion ◽

Volume Method ◽

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Benchmark 3D: A Monotone Nonlinear Finite Volume Method for Diffusion Equations on Polyhedral Meshes

Finite Volumes for Complex Applications VI Problems & Perspectives - Springer Proceedings in Mathematics ◽

10.1007/978-3-642-20671-9_97 ◽

2011 ◽

pp. 993-1003 ◽

Author(s):

Alexander Danilov ◽

Yuri Vassilevski

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Polyhedral Meshes ◽

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On positivity preservation in nonlinear finite volume method for multi-term fractional subdiffusion equation on polygonal meshes

Nonlinear Dynamics ◽

10.1007/s11071-018-4077-5 ◽

2018 ◽

Vol 92 (2) ◽

pp. 595-612 ◽

Author(s):

Xuehua Yang ◽

Qi Zhang ◽

Guangwei Yuan ◽

Zhiqiang Sheng

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Polygonal Meshes ◽

Positivity Preservation ◽

Subdiffusion Equation ◽

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Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

Multiscale Modeling and Simulation ◽

10.1137/15m1022537 ◽

2016 ◽

Vol 14 (4) ◽

pp. 1341-1376 ◽

Author(s):

David A. Barajas-Solano ◽

A. M. Tartakovsky

Keyword(s):

Boundary Conditions ◽

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Advection Diffusion ◽

Multiscale Finite Volume ◽

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A new finite volume method for the solution of convection-diffusion equations: analysis of stability and convergence

Communications in Numerical Methods in Engineering ◽

10.1002/(sici)1099-0887(199712)13:12<923::aid-cnm122>3.0.co;2-f ◽

1997 ◽

Vol 13 (12) ◽

pp. 923-940 ◽

Author(s):

E. Cordero ◽

L. De Biase ◽

V. Pennati

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Stability And Convergence ◽

Convection Diffusion ◽

Analysis Of Stability ◽

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A Monotone Non-linear Finite Volume Method for Advection-diffusion Equations and Multiphase Flows

ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery ◽

10.3997/2214-4609.20143223 ◽

2012 ◽

Author(s):

K. Nikitin ◽

Y. Vassilevski

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Multiphase Flows ◽

Diffusion Equations ◽

Advection Diffusion ◽

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A monotone nonlinear finite volume method for advection–diffusion equations on unstructured polyhedral meshes in 3D

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rjnamm.2010.022 ◽

2010 ◽

Vol 25 (4) ◽

Author(s):

K. Nikitin ◽

Yu. Vassilevski

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Polyhedral Meshes ◽

Advection Diffusion ◽

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