The Diamond Laplace for Polygonal and Polyhedral Meshes

AbstractWe present novel techniques for obtaining the basic estimates of virtual element methods in terms of the shape regularity of polygonal/polyhedral meshes. We also derive new error estimates for the Poisson problem in two and three dimensions.

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Diffusion problem on generalized polyhedral meshes

The Mimetic Finite Difference Method for Elliptic Problems ◽

10.1007/978-3-319-02663-3_12 ◽

2014 ◽

pp. 339-370

Author(s):

Lourenço Beirão da Veiga ◽

Konstantin Lipnikov ◽

Gianmarco Manzini

Keyword(s):

Diffusion Problem ◽

Polyhedral Meshes

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Interior penalty discontinuous Galerkin method on very general polygonal and polyhedral meshes

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2013.06.003 ◽

2014 ◽

Vol 255 ◽

pp. 432-440 ◽

Cited By ~ 11

Author(s):

Lin Mu ◽

Junping Wang ◽

Yanqiu Wang ◽

Xiu Ye

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Interior Penalty ◽

Polyhedral Meshes

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From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes

Lecture Notes in Computational Science and Engineering - Domain Decomposition Methods in Science and Engineering XVIII ◽

10.1007/978-3-642-02677-5_35 ◽

2009 ◽

pp. 315-322 ◽

Cited By ~ 13

Author(s):

Dylan Copeland ◽

Ulrich Langer ◽

David Pusch

Keyword(s):

Finite Element ◽

Domain Decomposition ◽

Boundary Element ◽

Finite Element Methods ◽

Decomposition Methods ◽

Domain Decomposition Methods ◽

Polyhedral Meshes ◽

Trefftz Finite Element

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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 ◽

Cited By ~ 2

Author(s):

Alexander Danilov ◽

Yuri Vassilevski

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Polyhedral Meshes ◽

Volume Method

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Two Nonlinear Positivity-Preserving Finite Volume Schemes for Three-Dimensional Heat Conduction Equations on General Polyhedral Meshes

Communications in Computational Physics ◽

10.4208/cicp.oa-2021-0011 ◽

2021 ◽

Vol 30 (4) ◽

pp. 1185-1215

Author(s):

global sci

Keyword(s):

Heat Conduction ◽

Finite Volume ◽

Three Dimensional ◽

Finite Volume Schemes ◽

Positivity Preserving ◽

Polyhedral Meshes

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Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equations

Partial Differential Equations - Computational Methods in Applied Sciences ◽

10.1007/978-1-4020-8758-5_2 ◽

2008 ◽

pp. 27-41 ◽

Cited By ~ 1

Author(s):

Yuri A. Kuznetsov

Keyword(s):

Finite Element ◽

Finite Element Methods ◽

Mixed Finite Element ◽

Mixed Finite Element Methods ◽

Diffusion Equations ◽

Polyhedral Meshes

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Approximations with piecewise constant fluxes for diffusion equations on polyhedral meshes: algorithms and applications

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2012-0019 ◽

2012 ◽

Vol 27 (4) ◽

Cited By ~ 2

Author(s):

O. Boyarkin ◽

E. Kikinzon ◽

Yu.A. Kuznetsov ◽

A. Prokopenko

Keyword(s):

Diffusion Equations ◽

Piecewise Constant ◽

Polyhedral Meshes

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Conservative high-order discontinuous Galerkin remap scheme on curvilinear polyhedral meshes

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109712 ◽

2020 ◽

Vol 420 ◽

pp. 109712 ◽

Cited By ~ 1

Author(s):

Konstantin Lipnikov ◽

Nathaniel Morgan

Keyword(s):

Discontinuous Galerkin ◽

High Order ◽

Polyhedral Meshes

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