The Shortest-Edge Duplication of Triangles
MATHEMATICS(2022)
摘要
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 alpha = pi/6. This bound does not depend on the shape of the initial triangle.
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关键词
triangulations, shortest edge, finite element method, triangle shape
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