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Article

Kolcun, Alexej ; Sysala, Stanislav
RTIN-based strategies for local mesh refinement. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 21-26, 2020. Institute of Mathematics CAS, Prague, 2021. pp. 59-68
MSC: 65D17, 65D18 | DOI: 10.21136/panm.2020.06
Keywords:
mesh refinement; longest-edge bisection; right-triangulated irregular network; balanced quadrant tree; homomorphic transformation
Summary:
Longest-edge bisection algorithms are often used for local mesh refinements within the finite element method in 2D. In this paper, we discuss and describe their conforming variant. A particular attention is devoted to the so-called Right-Triangulated Irregular Network (RTIN) based on isosceles right triangles and its tranformation to more general domains. We suggest to combine RTIN with a balanced quadrant tree (QuadTree) decomposition. This combination does not produce hanging nodes within the mesh refinements and could be extended to tetrahedral meshes in 3D.
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