## Global and local refinement techniques yielding nonobtuse tetrahedral partitions.(English)Zbl 1086.65116

A tetrahedron is said to be a path tetrahedron if its three edges, which do not meet at the same vertex are mutually orthogonal. The authors state a set of conditions on a tetrahedron $$T$$ which ensures the existence of a family of partitions of $$T$$ consisting of path tetrahedrons only [see M. Krizek and J. Pradlova, Numer. Methods Partial Differ. Equations 16, 327–334 (2000; Zbl 0957.65012)]. Considering a path tetrahedron $$ABCD$$ such that the edges $$AB, BC$$ and $$CD$$ are mutually orthogonal, the authors prove that there exists an infinite family of nonobtuse partitions of it into path tetrahedra that locally refine $$ABCD$$ in a neighbourhood of the vertex $$A$$.

### MSC:

 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35K15 Initial value problems for second-order parabolic equations

Zbl 0957.65012
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### References:

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