Abstract
First we introduce a mesh density function that is used to define a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse. Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the criterion function. Dividing this edge at its midpoint, we correspondingly bisect all simplices sharing this edge. Repeating this process, we construct a sequence of conforming nested simplicial meshes whose shape is determined by the mesh density function. We prove that the corresponding mesh size of the sequence tends to zero for d = 2, 3 as the bisection algorithm proceeds. It is also demonstrated numerically that the algorithm seems to produce only a finite number of similarity-distinct triangles.
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Hannukainen, A., Korotov, S., Křížek, M. (2010). On a Bisection Algorithm That Produces Conforming Locally Refined Simplicial Meshes. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_68
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DOI: https://doi.org/10.1007/978-3-642-12535-5_68
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