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Article

Hošek, Radim
The role of Sommerville tetrahedra in numerical mathematics. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Janov nad Nisou, June 19-24, 2016. Institute of Mathematics CAS, Prague, 2017. pp. 46-54
MSC: 51M04, 51M20, 65N30, 65N50 | DOI: 10.21136/panm.2016.06
Keywords:
simplicial tessellations; simplicial mesh; Sommerville tetrahedron; well-centered mesh; boundary-fitted mesh; high dimension
Summary:
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction by its direct generalization to any dimension.
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