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Strongly regular family of boundary-fitted tetrahedral meshes of bounded $$C^2$$ domains. (English) Zbl 1413.65424
Summary: We give a constructive proof that for any bounded domain of the class $$C^2$$ there exists a strongly regular family of boundary-fitted tetrahedral meshes. We adopt a refinement technique introduced by M. Křížek [Apl. Mat. 27, 46–75 (1982; Zbl 0488.73072)] and modify it so that a refined mesh is again boundary-fitted. An alternative regularity criterion based on similarity with the Sommerville tetrahedron is used and shown to be equivalent to other standard criteria. The sequence of regularities during the refinement process is estimated from below and shown to converge to a positive number by virtue of the convergence of $$q$$-Pochhammer symbol. The final result takes the form of an implication with an assumption that can be obviously fulfilled for any bounded $$C^2$$ domain.

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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