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The minimum angle condition for \(d\)-simplices. (English) Zbl 1446.65100

Summary: In this note we present a natural generalization of the minimum angle condition, commonly used in the finite element analysis for planar triangulations, to the case of simplicial meshes in any space dimension. The equivalence of this condition with some other mesh regularity conditions is proved.

MSC:

65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
41A05 Interpolation in approximation theory

References:

[1] Zlámal, M., On the finite element method, Numer. Math., 12, 394-409 (1968) · Zbl 0176.16001
[2] Ženíšek, A., The convergence of the finite element method for boundary value problems of a system of elliptic equations (in czech), Appl. Mat., 14, 355-377 (1969) · Zbl 0188.22604
[3] Brandts, J.; Korotov, S.; Křížek, M., On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions, Comput. Math. Appl., 55, 2227-2233 (2008) · Zbl 1142.65443
[4] Brandts, J.; Korotov, S.; Křížek, M., On the equivalence of ball conditions for simplicial finite elements in \(R^d\), Appl. Math. Lett., 22, 1210-1212 (2009) · Zbl 1173.52301
[5] Brandts, J.; Korotov, S.; Křížek, M., Generalization of the Zlámal condition for simplicial finite elements in \(R^d\), Appl. Math., 56, 417-424 (2011) · Zbl 1240.65327
[6] Ciarlet, P. G., The Finite Element Method for Elliptic Problems (1978), North-Holland: North-Holland Amsterdam · Zbl 0383.65058
[7] Eriksson, F., The law of sines for tetrahedra and \(n\)-simplices, Geom. Dedicata, 7, 71-80 (1978) · Zbl 0375.50008
[8] Gaddum, J. W., Distance sums on a sphere and angle sums in a simplex, Amer. Math. Monthly, 63, 91-96 (1956) · Zbl 0071.36304
[9] Hannukainen, A.; Korotov, S.; Křížek, M., On global and local mesh refinements by a generalized conforming bisection algorithm, J. Comput. Appl. Math., 235, 419-436 (2010) · Zbl 1207.65145
[10] Hannukainen, A.; Korotov, S.; Křížek, M., On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions, Sci. Comput. Program., 90, 34-41 (2014)
[11] Khademi, A.; Korotov, S.; Vatne, J. E., On the generalization of the Synge-Křížek maximum angle condition for d-simplices, J. Comput. Appl. Math., 358, 29-33 (2019) · Zbl 1426.65177
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