{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T04:31:07Z","timestamp":1791606667626,"version":"4.3.4"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>\n                    A modified finite difference approximation for interface problems in R\n                    <jats:sup>n<\/jats:sup>\n                    , n=1,2,3, is presented. The essence of the modification falls in the simultaneous discretization of any two normal components of the flux at the opposite faces of the finite volume. In this way, the continuous normal component of the flux through an interface is approximated by finite differences with second-order consistency. The derived scheme has a minimal (2n+1)-point stencil for problems in R\n                    <jats:sup>n<\/jats:sup>\n                    . Second-order convergence with respect to the discrete H\n                    <jats:sup>1<\/jats:sup>\n                    -norm is proved for a class of interface problems. Second-order pointwise convergence is observed in a series of numerical experiments with one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) interface problems. The numerical experiments presented demonstrate advantages of the new scheme compared with the known schemes which use arithmetic and harmonic averaging of the discontinuous diffusion coefficient.\n                  <\/jats:p>","DOI":"10.1137\/s1064827599353877","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1335-1351","source":"Crossref","is-referenced-by-count":35,"title":["A Modified Finite Volume Approximation of Second-Order Elliptic Equations with Discontinuous Coefficients"],"prefix":"10.1137","volume":"23","author":[{"given":"R.","family":"Ewing","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"O.","family":"Iliev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Lazarov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","volume-title":"Finite element solution of boundary value problems","author":"Axelsson O.","year":"1984"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385651"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0728022"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-99-01090-X"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1994-1203735-1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1080\/00207169208804111"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(97)00097-4"},{"key":"R8","unstructured":"O. P. Iliev,\n                      On second order accurate discretization of 3\u2010D elliptic problems with discontinuous coefficients and its fast solution with pointwise multi\u2010grid solver\n                      , IMA J. Numer. Anal., to appear."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02104764"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994264699"},{"key":"R11","first-page":"209","volume":"16","author":"Kondrat\u2019ev V.","year":"1967","journal-title":"Trudy Moskov. Mat. Ob\u0161\u010d."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1201\/9781482270211"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0732076"},{"key":"R14","volume-title":"Metody vychislitelnoi matematiki","author":"Marchuk G.","year":"1973"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2426(199803)14:2<193::AID-NUM4>3.0.CO;2-J"},{"key":"R16","unstructured":"A. Samarskii\u02d8, Teoriya raznostnykh skhem, Izdat. \u201cNauka\u201d, Moscow, 1977, 656\u2013058:3288"},{"key":"R17","unstructured":"A. A. Samarskii and V. B. Andreev,\n                      Difference Methods for Elliptic Equations\n                      , Nauka, Moscow, 1976 (in Russian)."},{"key":"R18","volume-title":"Conservative finite\u2010difference methods on general grids","author":"Shashkov Mikhail","year":"1996"},{"key":"R19","volume-title":"An analysis of the finite element method","author":"Strang Gilbert","year":"1973"},{"key":"R20","first-page":"5","volume":"1","author":"Tihonov A.","year":"1961","journal-title":"\u017d. Vy\u010disl. Mat. i Mat. Fiz."},{"key":"R21","first-page":"425","volume":"1","author":"Tihonov A.","year":"1961","journal-title":"\u017d. Vy\u010disl. Mat. i Mat. 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