{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T01:50:46Z","timestamp":1787709046664,"version":"build-2784847793"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. For approximating a convex function, although bilinear quadrilaterals are more efficient, linear triangles are more accurate and may be preferred in finite element computations; whereas for saddle-shaped functions, quadrilaterals may offer a higher-order approximation on a well-designed mesh. A surprising finding is different grid orientations may yield an order of magnitude improvement in approximation accuracy<\/jats:p>","DOI":"10.1137\/s106482759630406x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"198-217","source":"Crossref","is-referenced-by-count":35,"title":["Are Bilinear Quadrilaterals Better Than Linear Triangles?"],"prefix":"10.1137","volume":"22","author":[{"given":"E. F.","family":"D'Azevedo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0363(19961015)23:7<673::AID-FLD471>3.0.CO;2-P"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19980315)41:5<915::AID-NME318>3.0.CO;2-Y"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-874X(96)00057-1"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-874X(96)00065-0"},{"key":"R5","unstructured":"F. Bossen,\n                      Anisotropic Mesh Generation with Particles\n                      , Tech. report CMU\u2010CS\u201096\u2010134, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1996; also available from http:\/\/ltswww.epfl.ch\/ bossen\/meshing.html."},{"key":"R6","unstructured":"E. F. D\u2019Azevedo,\n                      On Optimal Triangulation for Piecewise Linear Approximation\n                      , Ph.D. thesis, Department of Computer Science, University of Waterloo, Waterloo, ON, Canada, 1989."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0912040"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0910064"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385784"},{"key":"R10","unstructured":"M. Fortin, M.\u2010G. Vallet, D. Poirier, and W. G. Habashi,\n                      Error Estimation and Directionally Adaptive Meshing\n                      , AIAA paper A94\u201030728, 25th Fluid Dynamics Conference, Colorado Springs, CO, 1994."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-874X(96)00063-7"},{"key":"R12","unstructured":"P. L. George and F. 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Sokolnikoff,\n                      Tensor Analysis, Theory and Applications to Geometry and Mechanics of Continua\n                      , 2nd ed., John Wiley, New York, 1964."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S106482759630406X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:35:52Z","timestamp":1787333752000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S106482759630406X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S106482759630406X"],"URL":"https:\/\/doi.org\/10.1137\/s106482759630406x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}