The Shortest-Edge Duplication of Triangles

Miguel Ángel Padrón, Francisco Perdomo, Ángel Plaza and José Pablo Suárez ()
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Miguel Ángel Padrón: IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain
Francisco Perdomo: IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain
Ángel Plaza: IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain
José Pablo Suárez: IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain

Mathematics, 2022, vol. 10, issue 19, 1-13

Abstract: We introduce a new triangle transformation, the shortest-edge (SE) duplication, as a natural way of mesh derefinement suitable to those meshes obtained by iterative application of longest-edge bisection refinement. Metric properties of the SE duplication of a triangle in the region of normalised triangles endowed with the Poincare hyperbolic metric are studied. The self-improvement of this transformation is easily proven, as well as the minimum angle condition. We give a lower bound for the maximum of the smallest angles of the triangles produced by the iterative SE duplication α = π 6 . This bound does not depend on the shape of the initial triangle.

Keywords: triangulations; shortest edge; finite element method; triangle shape (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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