{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T17:03:39Z","timestamp":1725555819640},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642125348"},{"type":"electronic","value":"9783642125355"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-12535-5_68","type":"book-chapter","created":{"date-parts":[[2010,5,8]],"date-time":"2010-05-08T15:53:31Z","timestamp":1273334011000},"page":"571-579","source":"Crossref","is-referenced-by-count":0,"title":["On a Bisection Algorithm That Produces Conforming Locally Refined Simplicial Meshes"],"prefix":"10.1007","author":[{"given":"Antti","family":"Hannukainen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergey","family":"Korotov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"K\u0159\u00ed\u017eek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"68_CR1","doi-asserted-by":"publisher","first-page":"571","DOI":"10.2307\/2007533","volume":"40","author":"A. Adler","year":"1983","unstructured":"Adler, A.: On the bisection method for triangles. Math. Comp.\u00a040, 571\u2013574 (1983)","journal-title":"Math. Comp."},{"key":"68_CR2","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1137\/S1064827597323373","volume":"22","author":"D.N. Arnold","year":"2000","unstructured":"Arnold, D.N., Mukherjee, A., Pouly, L.: Locally adapted tetrahedral meshes using bisection. SIAM J. Sci. Comput.\u00a022, 431\u2013448 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"68_CR3","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/0899-8248(91)90006-G","volume":"3","author":"E. B\u00e4nsch","year":"1991","unstructured":"B\u00e4nsch, E.: Local mesh refinement in 2 and 3 dimensions. IMPACT Comp. Sci. Engrg.\u00a03, 181\u2013191 (1991)","journal-title":"IMPACT Comp. Sci. Engrg."},{"key":"68_CR4","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1145\/2701.2705","volume":"10","author":"A. Eiger","year":"1984","unstructured":"Eiger, A., Sikorski, K., Stenger, F.: A bisection method for systems of nonlinear equations. ACM Trans. Math. Software\u00a010, 367\u2013377 (1984)","journal-title":"ACM Trans. Math. Software"},{"key":"68_CR5","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1142\/S0218202594000194","volume":"4","author":"K. Eriksson","year":"1994","unstructured":"Eriksson, K.: An adaptive finite element method with efficient maximum norm error control for elliptic problems. Math. Models Methods Appl. Sci.\u00a04, 313\u2013329 (1994)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"68_CR6","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.2307\/2006341","volume":"32","author":"R.B. Kearfott","year":"1978","unstructured":"Kearfott, R.B.: A proof of convergence and an error bound for the method of bisection in R\n                  \n                    n\n                  . Math. Comp.\u00a032, 1147\u20131153 (1978)","journal-title":"Math. Comp."},{"key":"68_CR7","doi-asserted-by":"publisher","first-page":"1687","DOI":"10.1134\/S0965542508090170","volume":"48","author":"S. Korotov","year":"2008","unstructured":"Korotov, S., K\u0159\u00ed\u017eek, M., Krop\u00e1\u010d, A.: Strong regularity of a family of face-to-face partitions generated by the longest-edge bisection algorithm. Comput. Math. Math. Phys.\u00a048, 1687\u20131698 (2008)","journal-title":"Comput. Math. Math. Phys."},{"key":"68_CR8","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/BF00047538","volume":"9","author":"M. K\u0159\u00ed\u017eek","year":"1987","unstructured":"K\u0159\u00ed\u017eek, M., Neittaanm\u00e4ki, P.: On superconvergence techniques. Acta Appl. Math.\u00a09, 175\u2013198 (1987)","journal-title":"Acta Appl. Math."},{"key":"68_CR9","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1002\/(SICI)1098-2426(199703)13:2<201::AID-NUM5>3.0.CO;2-T","volume":"13","author":"M. K\u0159\u00ed\u017eek","year":"1997","unstructured":"K\u0159\u00ed\u017eek, M., Strouboulis, T.: How to generate local refinements of unstructured tetrahedral meshes satisfying a regularity ball condition. Numer. Methods Partial Differential Equations\u00a013, 201\u2013214 (1997)","journal-title":"Numer. Methods Partial Differential Equations"},{"key":"68_CR10","doi-asserted-by":"publisher","first-page":"141","DOI":"10.2307\/2153566","volume":"63","author":"A. Liu","year":"1994","unstructured":"Liu, A., Joe, B.: On the shape of tetrahedra from bisection. Math. Comp.\u00a063, 141\u2013154 (1994)","journal-title":"Math. Comp."},{"key":"68_CR11","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1137\/0916074","volume":"16","author":"A. Liu","year":"1995","unstructured":"Liu, A., Joe, B.: Quality of local refinement of tetrahedral meshes based on bisection. SIAM J. Sci. Comput.\u00a016, 1269\u20131291 (1995)","journal-title":"SIAM J. Sci. Comput."},{"key":"68_CR12","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1002\/nme.1620200412","volume":"20","author":"M.-C. Rivara","year":"1984","unstructured":"Rivara, M.-C.: Algorithms for refining triangular grids suitable for adaptive and multigrid techniques. Internat. J. Numer. Methods Engrg.\u00a020, 745\u2013756 (1984)","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"68_CR13","doi-asserted-by":"publisher","first-page":"2889","DOI":"10.1002\/nme.1620281212","volume":"28","author":"M.-C. Rivara","year":"1989","unstructured":"Rivara, M.-C.: Selective refinement\/derefinement algorithms for sequences of nested triangulations. Internat. J. Numer. Methods Engrg.\u00a028, 2889\u20132906 (1989)","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"68_CR14","doi-asserted-by":"publisher","first-page":"2218","DOI":"10.1016\/j.apnum.2008.12.011","volume":"59","author":"M.-C. Rivara","year":"2009","unstructured":"Rivara, M.-C.: Lepp-algorithms, applications and mathematical properties. Appl. Numer. Math.\u00a059, 2218\u20132235 (2009)","journal-title":"Appl. Numer. Math."},{"key":"68_CR15","doi-asserted-by":"publisher","first-page":"1485","DOI":"10.1090\/S0025-5718-96-00772-7","volume":"65","author":"M.-C. Rivara","year":"1996","unstructured":"Rivara, M.-C., Iribarren, G.: The 4-triangles longest-side partition and linear refinement algorithm. Math. Comp.\u00a065, 1485\u20131502 (1996)","journal-title":"Math. Comp."},{"key":"68_CR16","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1002\/cnm.1630080502","volume":"8","author":"M.-C. Rivara","year":"1992","unstructured":"Rivara, M.-C., Levin, C.: A 3D refinement algorithm suitable for adaptive and multigrid techniques. Comm. Appl. Numer. Methods Engrg.\u00a08, 281\u2013290 (1992)","journal-title":"Comm. Appl. Numer. Methods Engrg."},{"key":"68_CR17","doi-asserted-by":"publisher","first-page":"390","DOI":"10.2307\/2005558","volume":"29","author":"I.G. Rosenberg","year":"1975","unstructured":"Rosenberg, I.G., Stenger, F.: A lower bound on the angles of triangles constructed by bisection of the longest side. Math. Comp.\u00a029, 390\u2013395 (1975)","journal-title":"Math. Comp."},{"key":"68_CR18","doi-asserted-by":"publisher","first-page":"722","DOI":"10.2307\/2006307","volume":"33","author":"K. Sikorski","year":"1979","unstructured":"Sikorski, K.: A three dimensional analogue to the method of bisections for solving nonlinear equations. Math. Comp.\u00a033, 722\u2013738 (1979)","journal-title":"Math. Comp."},{"key":"68_CR19","doi-asserted-by":"publisher","first-page":"717","DOI":"10.2307\/2006306","volume":"33","author":"M. Stynes","year":"1979","unstructured":"Stynes, M.: On faster convergence of the bisection method for certain triangles. Math. Comp.\u00a033, 717\u2013721 (1979)","journal-title":"Math. Comp."},{"key":"68_CR20","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.2307\/2006385","volume":"35","author":"M. Stynes","year":"1980","unstructured":"Stynes, M.: On faster convergence of the bisection method for all triangles. Math. Comp.\u00a035, 1195\u20131201 (1980)","journal-title":"Math. Comp."}],"container-title":["Lecture Notes in Computer Science","Large-Scale Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-12535-5_68.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T11:42:42Z","timestamp":1619782962000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-12535-5_68"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642125348","9783642125355"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-12535-5_68","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}