{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:28:24Z","timestamp":1787336904483,"version":"build-2736575974"},"reference-count":13,"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>Many real-world problems are successfully modeled by partial differential equations. Many numerical solvers for these problems use triangular and tetrahedral meshes to accurately model complex geometries. Such problems often involve shocks and discontinuities, and it is important to devise interpolation methods that can accurately approximate solutions containing such features. These interpolants are required for the postprocessing of the solution, e.g., for visualization and to recover solution values at arbitrary points over the numerical domain. This paper describes a triangle-based quadratic interpolant that is \"data-bounded\" and so will not create any values outside of the range of the existing data points. The method is compared with the standard quadratic interpolant and extended to the case of quadratic tetrahedral elements.<\/jats:p>","DOI":"10.1137\/s1064827597317636","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"177-197","source":"Crossref","is-referenced-by-count":4,"title":["A Data-Bounded Quadratic Interpolant on Triangles and Tetrahedra"],"prefix":"10.1137","volume":"22","author":[{"given":"Martin","family":"Berzins","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"R. Abgrall,\n                      Design of an Essentially Non\u2010Oscillatory Reconstruction Procedure on Finite\u2010Element Type Meshes\n                      , ICASE report 91\u201084, 1991;"},{"key":"R1","unstructured":"revised form INRIA report 1592, 1992."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9045(73)90020-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9045(74)90002-1"},{"key":"R4","unstructured":"T. G. Barth,\n                      On Unstructured Grids and Solvers\n                      , Technical report, von Karman Institute for Fluid Dynamics, Lecture Series 1990\u201003, 1990."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(95)00007-H"},{"key":"R6","unstructured":"K. W. Brodlie and P. Mashwama,\n                      Controlled interpolation for scientific visualization\n                      , in Scientific Visualization, in Proceedings of IEEE Conference on Visualization, G. M. Nielson et al., eds., IEEE Computer Society, Los Alamitos, CA, 1997, pp. 253\u2013275."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(92)90173-V"},{"key":"R8","unstructured":"R. H. Gallagher,\n                      Finite Element Analysis Fundamentals\n                      , Prentice\u2010Hall, London, 1975."},{"key":"R9","unstructured":"C. Johnson,\n                      Numerical Solutions of p. d. e.s by the Finite Element Methods\n                      , Cambridge University Press, Cambridge, UK, 1988."},{"key":"R10","first-page":"723","volume":"385","author":"Pratt P.","year":"1997","journal-title":"Comput. Graphics","ISSN":"https:\/\/id.crossref.org\/issn\/0097-8493","issn-type":"print"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.2514\/3.13101"},{"key":"R12","unstructured":"O. C. Zienkiewicz and R. L. Taylor,\n                      The Finite Element Method\n                      , McGraw\u2010Hill, London, 1989."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827597317636","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\/S1064827597317636"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827597317636"],"URL":"https:\/\/doi.org\/10.1137\/s1064827597317636","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}