Geodesic
Justification of asymptotic stability of the triangulation algorithm for a~three-dimensional domain
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 2, pp. 123-136

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An algorithm of triangulation construction (the subdivision into tetrahedrons) for a three-dimensional bounded domain with a smooth curvilinear boundary is considered. The algorithm starts on a given coarsest triangulation. The consequent finer triangulations are recurrently constructed by the subdivision of tetrahedrons of the previous level into 8 parts with correction of the location of vertices near the boundary to approximate the boundary. To evaluate the quality of a triangulation a certain quantitative criterion is used. It is proved that a successful (in the sense of this criterion) initial triangulation moderately detailed guarantees good quality of the consequent finer triangulations under arbitrary number of recurrent implementations of subdivision algorithm. 
@article{SJVM_2000_3_2_a3,
     author = {L. V. Gilyova and V. V. Shaidurov},
     title = {Justification of asymptotic stability of the triangulation algorithm for a~three-dimensional domain},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {123--136},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2000_3_2_a3/}
}
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L. V. Gilyova; V. V. Shaidurov. Justification of asymptotic stability of the triangulation algorithm for a~three-dimensional domain. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 2, pp. 123-136. http://geodesic.mathdoc.fr/item/SJVM_2000_3_2_a3/