{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:18Z","timestamp":1787337018752,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>One-dimensional, second-order finite-difference approximations of the derivative are constructed which satisfy a global conservation law. Creating a second-order approximation away from the boundary is simple, but obtaining appropriate behavior near the boundary is difficult, even in one dimension on a uniform grid. In this article we exhibit techniques that allow the construction of discrete versions of the divergence and gradient operator that have high-order approximations at the boundary. We construct such discretizations in the one-dimensional situation which have fourth-order approximation both on the boundary and in the interior. The precision of the high-order mimetic schemes in this article is as high as possible at the boundary points (with respect to the bandwidth parameter). This guarantees an overall high order of accuracy. Furthermore, the method described for the calculation of the approximations uses matrix analysis to streamline the various mimetic conditions. This contributes to a marked clarity with respect to earlier approaches.<\/jats:p>\n                  <jats:p>This is a crucial preliminary step in creating higher-order approximations of the divergence and gradient for nonuniform grids in higher dimensions.<\/jats:p>","DOI":"10.1137\/s0895479801398025","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"128-142","source":"Crossref","is-referenced-by-count":62,"title":["A Matrix Analysis Approach to Higher-Order Approximations for Divergence and Gradients Satisfying a Global Conservation Law"],"prefix":"10.1137","volume":"25","author":[{"given":"J. E.","family":"Castillo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. D.","family":"Grone","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144597328341"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1057"},{"key":"R3","unstructured":"J. E. Castillo,\n                      A family of, including boundary, mimetic schemes from second to sixth order\n                      , in preparation."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(00)00033-7"},{"key":"R5","unstructured":"J. E. Castillo, J. M. Hyman, M. J. Shashkov, and S. Steinberg,\n                      High\u2010order mimetic finite\u2010difference schemes on non\u2010uniform grids\n                      , in ICOSAHOM 95, Houston, TX, 1996, pp. 347\u2013361."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(95)00136-M"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90230-K"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6225"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5633"},{"key":"R10","volume-title":"Conservative finite\u2010difference methods on general grids","author":"Shashkov Mikhail","year":"1996"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0257"},{"key":"R12","first-page":"0","volume":"64","author":"Olsson Pelle","year":"1995","journal-title":"Math. Comp."},{"key":"R13","volume-title":"Mathematical aspects of finite elements in partial differential equations","author":"de Boor Carl","year":"1974"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1005"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479801398025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:40:58Z","timestamp":1787334058000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479801398025"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479801398025"],"URL":"https:\/\/doi.org\/10.1137\/s0895479801398025","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}