Special meshes and higher-order schemes for singularly perturbed boundary value problems.
Vulanović, Relja (2001)
Novi Sad Journal of Mathematics
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Displaying similar documents to “The role of Sommerville tetrahedra in numerical mathematics”
Special meshes and higher-order schemes for singularly perturbed boundary value problems.
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...
High-order compact implicit difference methods for parabolic equations in geodynamo simulation.
Liu, Don, Kuang, Weijia, Tangborn, Andrew (2009)
Advances in Mathematical Physics
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Curved elements in the finite element method
Zlámal, Miloš
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Numerical experiments with different schemes for a singularly perturbed problem.
Herceg, Dragoslav, Surla, Katarina, Radeka, Ivana, Maličić, Helena (2001)
Novi Sad Journal of Mathematics
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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...