Red refinements of simplices into congruent subsimplices

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...

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Detalles Bibliográficos
Autores: Korotov, S., Krizek, M.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2014
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/111
Acceso en línea:http://hdl.handle.net/20.500.11824/111
Access Level:acceso abierto
Palabra clave:Computational mechanics
Finite element method
Adaptivity
Higher-dimensional
Mesh refinement
Red refinement
Sommerville tetrahedron
Subtetrahedra
Geometry
Descripción
Sumario: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 the original one.