{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:24:06Z","timestamp":1787329446798,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We introduce a new higher order scheme for computing a tangentially stabilized curve shortening flow with a driving force represented by an intrinsic partial differential equation for an evolving curve position vector. Our new scheme is a combination of the explicit forward Euler and the fully implicit backward Euler schemes. At any discrete time step, the solution is found efficiently using a few semi-implicit iterations. Basic properties of the new scheme are proved in the paper, and its precision is tested by comparing the results with known analytical solutions. For any choice of the time step, the new higher order scheme gives exact radius of evolving uniformly discretized circles in case of flow by curvature and in case of rotation by a constant tangential velocity. Such properties do not hold for other schemes solving flow by mean curvature like the classical explicit, semi-implicit, or fully implicit schemes. In general, the scheme is second order accurate, which is shown by comparing a numerically evolving encompassed area with known analytical expression. The behavior of the scheme is discussed on representative examples, and its advantages with respect to the balance between CPU time and precision are shown.<\/jats:p>","DOI":"10.1137\/100795309","type":"journal-article","created":{"date-parts":[[2011,9,16]],"date-time":"2011-09-16T02:23:43Z","timestamp":1316139823000},"page":"2277-2294","source":"Crossref","is-referenced-by-count":20,"title":["A Higher Order Scheme for a Tangentially Stabilized Plane Curve Shortening Flow with a Driving Force"],"prefix":"10.1137","volume":"33","author":[{"given":"Martin","family":"Bala\u017eovjech","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karol","family":"Mikula","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,9,15]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01041068"},{"key":"R2","unstructured":"M. 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Mikula,\n                      A higher order scheme for the curve shortening flow of plane curves\n                      , in Proceedings of ALGORITMY 2009 - Conference on Scientific Computing, Podbansk\u00e9, Slovakia, 2009, Publishing House of STU, Bratislava, Slovakia, 2009, pp. 165\u2013175."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/060653974"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007979827043"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s005260050076"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202594000339"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142998337533"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1214439902"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1214441371"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1170"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00133570"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00379537"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167390"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594261905"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139999359288"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/mma.514"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-004-0131-6"},{"key":"R18","unstructured":"K. Mikula and D. \u0160ev\u010dovi\u010d,\n                      Tangentially stabilized Lagrangean algorithm for elastic curve evolution driven by intrinsic Laplacian of curvature\n                      , in Proceedings of ALGORITMY 2005 - Conference on Scientific Computing, Podbansk\u00e9, Slovakia, 2005, Publishing House of STU, Bratislava, Slovakia, 2005, pp. 32\u201341."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.2009.08.169"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"S. Osher and R. Fedkiw,\n                      Level Set Methods and Dynamic Implicit Surfaces\n                      , Springer, New York, 2003.","DOI":"10.1007\/b98879"},{"key":"R21","unstructured":"W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,\n                      Numerical Recipes in C\n                      , Cambridge University Press, Cambridge, 1992."},{"key":"R22","unstructured":"J. A. Sethian,\n                      Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science\n                      , Cambridge Monogr. Appl. Comput. Math. 3, Cambridge University Press, Cambridge, 1999."},{"key":"R23","unstructured":"D. \u0160ev\u010dovi\u010d and S. Yazaki,\n                      Evolution of plane curves with a curvature adjusted tangential velocity\n                      , Japan J. Indust. Appl. Math., to appear."},{"key":"R24","first-page":"913","volume":"43","author":"Yazaki S.","year":"2007","journal-title":"Kybernetika (Prague)"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100795309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:17:29Z","timestamp":1787325449000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100795309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":24,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100795309"],"URL":"https:\/\/doi.org\/10.1137\/100795309","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}