{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T16:20:28Z","timestamp":1732033228630},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,2,24]],"date-time":"2010-02-24T00:00:00Z","timestamp":1266969600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2011,1]]},"DOI":"10.1007\/s00366-010-0176-8","type":"journal-article","created":{"date-parts":[[2010,2,23]],"date-time":"2010-02-23T05:30:54Z","timestamp":1266903054000},"page":"3-15","source":"Crossref","is-referenced-by-count":4,"title":["A mesh optimization algorithm to decrease the maximum interpolation error of linear triangular finite elements"],"prefix":"10.1007","volume":"27","author":[{"given":"U.","family":"Hetmaniuk","sequence":"first","affiliation":[]},{"given":"P.","family":"Knupp","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,2,24]]},"reference":[{"issue":"4","key":"176_CR1","first-page":"223","volume":"7","author":"A Agouzal","year":"1999","unstructured":"Agouzal A, Lipnikov K, Vassilevski Y (1999) Adaptive generation of quasi-optimal tetrahedral meshes. East West J Numer Math 7(4):223\u2013244","journal-title":"East West J Numer Math"},{"key":"176_CR2","unstructured":"Alauzet F, Frey P (2003) Estimation d\u2019erreur g\u00e9om\u00e9trique et m\u00e9triques anisotropes pour l\u2019adaptation de maillage. Partie II: exemples d\u2019applications. Technical Report 4789, INRIA"},{"key":"176_CR3","unstructured":"Apel T, Berzins M, Jimack P, Kunert G, Plaks A, Tsukerman I, Walkley M (2000) Mesh shape and anisotropic elements: Theory and practice. In: The mathematics of finite elements and applications, vol 10. Elsevier, Amsterdam, pp 367\u2013376"},{"key":"176_CR4","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1137\/0713021","volume":"13","author":"I Babu\u0161ka","year":"1976","unstructured":"Babu\u0161ka I, Aziz AK (1976) On the angle condition in the finite element method. SIAM J Numer Anal 13:214\u2013226","journal-title":"SIAM J Numer Anal"},{"key":"176_CR5","unstructured":"BAMG, Bidimensional anisotropic mesh generator. http:\/\/pauillac.inria.fr\/cdrom\/www\/bamg\/eng.htm"},{"key":"176_CR6","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1137\/S0036142994265292","volume":"34","author":"R Bank","year":"1997","unstructured":"Bank R, Smith R (1997) Mesh smoothing using a posteriori error estimates. SIAM J Numer Anal 34:979\u2013997","journal-title":"SIAM J Numer Anal"},{"key":"176_CR7","doi-asserted-by":"crossref","first-page":"2313","DOI":"10.1137\/S0036142901398751","volume":"41","author":"R Bank","year":"2003","unstructured":"Bank R, Xu J (2003) Asymptotically exact a posteriori error estimators, part II: general unstructured grids. SIAM J Numer Anal 41:2313\u20132332","journal-title":"SIAM J Numer Anal"},{"key":"176_CR8","doi-asserted-by":"crossref","first-page":"4119","DOI":"10.1002\/(SICI)1097-0207(19971130)40:22<4119::AID-NME254>3.0.CO;2-R","volume":"40","author":"G Buscaglia","year":"1997","unstructured":"Buscaglia G, Dari E (1997) Anisotropic mesh optimization and its application in adaptivity. Int J Numer Meth Eng 40:4119\u20134136","journal-title":"Int J Numer Meth Eng"},{"key":"176_CR9","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1137\/S0036142903433492","volume":"43","author":"W Cao","year":"2005","unstructured":"Cao W (2005) On the error of linear interpolation and the orientation, aspect ratio, and internal angles of a triangle. SIAM J Numer Anal 43:19\u201340","journal-title":"SIAM J Numer Anal"},{"key":"176_CR10","unstructured":"Chen L (2004) Mesh smoothing schemes based on optimal Delaunay triangulations. In: Proceedings of 13th international meshing roundtable"},{"key":"176_CR11","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1090\/S0025-5718-06-01896-5","volume":"76","author":"L Chen","year":"2007","unstructured":"Chen L, Sun P, Xu J (2007) Optimal anisotropic meshes for minimizing interpolation errors in L p -norm. Math Comp 76:179\u2013204","journal-title":"Math Comp"},{"key":"176_CR12","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.apnum.2005.03.001","volume":"56","author":"F Courty","year":"2006","unstructured":"Courty F, Leservoisier D, George PL, Dervieux A (2006) Continuous metric and mesh adaptation. Appl Numer Math 56:117\u2013145","journal-title":"Appl Numer Math"},{"key":"176_CR13","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1137\/0910064","volume":"10","author":"E D\u2019Azevedo","year":"1989","unstructured":"D\u2019Azevedo E, Simpson R (1989) On optimal interpolation triangle incidences. SIAM J Sci Comput 10:1063\u20131075","journal-title":"SIAM J Sci Comput"},{"key":"176_CR14","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1002\/fld.357","volume":"39","author":"J Dompierre","year":"2002","unstructured":"Dompierre J, Vallet MG, Bourgault Y, Fortin M, Habashi W (2002) Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver independent CFD. Part III: unstructured meshes. Int J Numer Meth Fluids 39:675\u2013702","journal-title":"Int J Numer Meth Fluids"},{"key":"176_CR15","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0307-904X(76)90005-6","volume":"1","author":"C Felippa","year":"1976","unstructured":"Felippa C (1976) Optimization of finite element grids by direct energy search. Appl Math Model 1:93\u201396","journal-title":"Appl Math Model"},{"key":"176_CR16","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1002\/(SICI)1097-0207(20000210)47:4<887::AID-NME804>3.0.CO;2-H","volume":"47","author":"D Field","year":"2000","unstructured":"Field D (2000) Qualitative measures for initial meshes. Int J Numer Meth Eng 47:887\u2013906","journal-title":"Int J Numer Meth Eng"},{"key":"176_CR17","unstructured":"Fletcher R (1987) Practical methods of optimization. Wiley, New York"},{"key":"176_CR18","doi-asserted-by":"crossref","first-page":"5068","DOI":"10.1016\/j.cma.2004.11.025","volume":"194","author":"P Frey","year":"2005","unstructured":"Frey P, Alauzet F (2005) Anisotropic mesh adaptation for CFD computations. Comput Methods Appl Mech Eng 194:5068\u20135082","journal-title":"Comput Methods Appl Mech Eng"},{"key":"176_CR19","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1145\/1132973.1132979","volume":"32","author":"W Hager","year":"2006","unstructured":"Hager W, Zhang H (2006) Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent. ACM Trans Math Softw 32:113\u2013137","journal-title":"ACM Trans Math Softw"},{"key":"176_CR20","unstructured":"Hetmaniuk U, Knupp P (2008) Mesh optimization algorithms to decrease the linear interpolation error. SAND Report"},{"key":"176_CR21","first-page":"276","volume":"1","author":"W Huang","year":"2006","unstructured":"Huang W (2006) Mathematical principles of anisotropic mesh adaptation. Commun Comput Phys 1:276\u2013310","journal-title":"Commun Comput Phys"},{"key":"176_CR22","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/S0965-9978(02)00077-7","volume":"33","author":"P Jimack","year":"2002","unstructured":"Jimack P, Mahmood R, Walkley M, Berzins M (2002) A multilevel approach for obtaining locally optimal finite element meshes. Adv Eng Softw 33:403\u2013415","journal-title":"Adv Eng Softw"},{"key":"176_CR23","unstructured":"Lag\u00fce JF (2006) Optimisation de maillage bas\u00e9e sur une erreur locale d\u2019interpolation. PhD thesis, Universit\u00e9 de Paris VI"},{"key":"176_CR24","unstructured":"Mesquite, Mesh quality improvement toolkit. See http:\/\/www.cs.sandia.gov\/optimization\/knupp\/Mesquite.html"},{"key":"176_CR25","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1002\/nme.1196","volume":"62","author":"JF Remacle","year":"2005","unstructured":"Remacle JF, Li X, Shephard M, Flaherty J (2005) Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods. Int J Numer Meth Eng 62:899\u2013923","journal-title":"Int J Numer Meth Eng"},{"key":"176_CR26","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1137\/0729017","volume":"29","author":"S Rippa","year":"1992","unstructured":"Rippa S (1992) Long and thin triangles can be good for linear interpolation. SIAM J Numer Anal 29:257\u2013270","journal-title":"SIAM J Numer Anal"},{"key":"176_CR27","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1002\/fld.336","volume":"40","author":"P Roe","year":"2002","unstructured":"Roe P, Nishikawa H (2002) Adaptive grid generation by minimizing residuals. Int J Numer Meth Fluids 40:121\u2013136","journal-title":"Int J Numer Meth Fluids"},{"key":"176_CR28","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1137\/S0036142996313932","volume":"35","author":"Y Tourigny","year":"1998","unstructured":"Tourigny Y, H\u00fclsemann F (1998) A new moving mesh algorithm for the finite element solution of variational problems. SIAM J Numer Anal 35:1416\u20131438","journal-title":"SIAM J Numer Anal"},{"key":"176_CR29","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s10915-004-4614-x","volume":"24","author":"Y Tourigny","year":"2005","unstructured":"Tourigny Y (2005) The optimisation of the mesh in first-order systems least-squares methods. J Sci Comput 24:219\u2013245","journal-title":"J Sci Comput"},{"key":"176_CR30","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1002\/nme.2036","volume":"72","author":"MG Vallet","year":"2007","unstructured":"Vallet MG, Manole C, Dompierre J, Dufour S, Guibault F (2007) Numerical comparison of some Hessian recovery techniques. Int J Numer Meth Eng 72:987\u20131007","journal-title":"Int J Numer Meth Eng"},{"key":"176_CR31","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1002\/fld.302","volume":"40","author":"M Walkley","year":"2002","unstructured":"Walkley M, Jimack P, Berzins M (2002) Anisotropic adaptivity for the finite element solutions of three-dimensional convection-dominated problems. Int J Numer Meth Fluids 40:551\u2013559","journal-title":"Int J Numer Meth Fluids"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-010-0176-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00366-010-0176-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-010-0176-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T10:44:43Z","timestamp":1559040283000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00366-010-0176-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,24]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["176"],"URL":"https:\/\/doi.org\/10.1007\/s00366-010-0176-8","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,24]]}}}