{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:32:57Z","timestamp":1776832377844,"version":"3.51.2"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"223","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>This paper contains error estimates for covolume discretizations of Maxwell\u2019s equations in three space dimensions. Several estimates are proved. First, an estimate for a semi-discrete scheme is given. Second, the estimate is extended to cover the classical interlaced time marching technique. Third, some of our unstructured mesh results are specialized to rectangular meshes, both uniform and nonuniform. By means of some additional analysis it is shown that the spatial convergence rate is one order higher than for the unstructured case.<\/p>","DOI":"10.1090\/s0025-5718-98-00971-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"947-963","source":"Crossref","is-referenced-by-count":56,"title":["Convergence analysis of a covolume scheme for Maxwell\u2019s equations in three dimensions"],"prefix":"10.1090","volume":"67","author":[{"given":"R.","family":"Nicolaides","sequence":"first","affiliation":[]},{"given":"D.-Q.","family":"Wang","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","series-title":"Studies in Mathematics and its Applications, Vol. 4","isbn-type":"print","volume-title":"The finite element method for elliptic problems","author":"Ciarlet, Philippe G.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0444850287"},{"key":"2","series-title":"Grundlehren der Mathematischen Wissenschaften","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66165-5","volume-title":"Inequalities in mechanics and physics","volume":"219","author":"Duvaut, G.","year":"1976","ISBN":"https:\/\/id.crossref.org\/isbn\/3540073272"},{"key":"3","doi-asserted-by":"crossref","unstructured":"R. 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Ziolkowski, A three dimensional modified finite volume technique for Maxwell\u2019s equations, Electromagnetics, Vol. 10, 1990, pp. 147-161.","DOI":"10.1080\/02726349008908233"},{"key":"10","doi-asserted-by":"crossref","unstructured":"B.J. McCartin and J.F. Dicello, Three dimensional finite difference frequency domain scattering computation using the Control Region Approximation, IEEE Trans. Magnetics, Vol. 25, No. 4, 1989, pp. 3092-3094.","DOI":"10.1109\/20.34378"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1137\/0731021","article-title":"A convergence analysis of Yee\u2019s scheme on nonuniform grids","volume":"31","author":"Monk, Peter","year":"1994","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"12","doi-asserted-by":"crossref","unstructured":"Peter Monk and Endre Suli, Error estimates for Yee\u2019s method on nonuniform grids, IEEE Trans. Magnetics, Vol 30, 1994, pp. 3200-3203.","DOI":"10.1109\/20.312618"},{"issue":"1","key":"13","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1137\/0729003","article-title":"Direct discretization of planar div-curl problems","volume":"29","author":"Nicolaides, R. A.","year":"1992","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"14","doi-asserted-by":"crossref","unstructured":"R.A. Nicolaides, Flow discretization by complementary volume techniques, AIAA paper 89-1978, Proceedings of 9th AIAA CFD Meeting, Buffalo, NY, June 1989.","DOI":"10.2514\/6.1989-1978"},{"issue":"6","key":"15","doi-asserted-by":"publisher","first-page":"1579","DOI":"10.1137\/0729091","article-title":"Analysis and convergence of the MAC scheme. I. The linear problem","volume":"29","author":"Nicolaides, R. A.","year":"1992","journal-title":"SIAM J. Numer. 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