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Displaying similar documents to “The role of Sommerville tetrahedra in numerical mathematics”

On simplicial red refinement in three and higher dimensions

Korotov, Sergey, Křížek, Michal

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We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to...

Finite element method on 3D mesh with layer structure - application on flow and transport in porous media

Hokr, Milan, Wasserbauer, Vladimír

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We introduce a formulation of the finite element method (FEM) adapted to typical geometry of groundwater problems. The three-dimensional domain is discretized in the following way: the projection to the horizontal plane is a triangulation (unstructured mesh) and the mesh is composed of layers in the space. Thus there is need to define finite elements on trilateral prims. We show an alternative numerical solution of porous media (potential) flow by means of combining the FEM on 2D triangle...

A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations

Abigail Wacher (2013)

Open Mathematics

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We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers’ equation and the porous medium...

Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes

Dana Kotorová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this work we describe two schemes for solving level set equation in 3D with a method based on finite volumes. These schemes use the so-called dual volumes as in [Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations Algoritmy 2009 (2009), 51–60.], [Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes Journal of Computational Physics 228, 16 (2009), 5763–5786.], where they are used for the nonlinear...

Description of the multi-dimensional finite volume solver EULER

Pavel Šolín, Karel Segeth (2002)

Applications of Mathematics

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This paper is aimed at the description of the multi-dimensional finite volume solver EULER, which has been developed for the numerical solution of the compressible Euler equations during several last years. The present overview of numerical schemes and the explanation of numerical techniques and tricks which have been used for EULER could be of certain interest not only for registered users but also for numerical mathematicians who have decided to implement a finite volume solver themselves....