{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T01:10:15Z","timestamp":1732669815567,"version":"3.28.2"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Mathematics with Applications"],"published-print":{"date-parts":[[2024,11]]},"DOI":"10.1016\/j.camwa.2024.08.016","type":"journal-article","created":{"date-parts":[[2024,8,24]],"date-time":"2024-08-24T00:44:59Z","timestamp":1724460299000},"page":"18-30","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A difference finite element method based on the conforming P1(x,y)\u00d7Q1(z,s) element for the 4D Poisson equation"],"prefix":"10.1016","volume":"174","author":[{"given":"Yaru","family":"Liu","sequence":"first","affiliation":[]},{"given":"Yinnian","family":"He","sequence":"additional","affiliation":[]},{"given":"Dongwoo","family":"Sheen","sequence":"additional","affiliation":[]},{"given":"Xinlong","family":"Feng","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.camwa.2024.08.016_br0010","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/num.1690030307","article-title":"Fourth-order finite difference methods for three-dimensional general linear elliptic problems with variable coefficients","volume":"3","author":"Ananthakrishnaiah","year":"1987","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"2","key":"10.1016\/j.camwa.2024.08.016_br0020","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1137\/S0036142994262585","article-title":"Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences","volume":"34","author":"Arbogast","year":"1997","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"10.1016\/j.camwa.2024.08.016_br0030","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1051\/m2an\/1996300404451","article-title":"Connection between finite volume and mixed finite element methods","volume":"30","author":"Baranger","year":"1996","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"issue":"4","key":"10.1016\/j.camwa.2024.08.016_br0040","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1093\/imanum\/dri018","article-title":"Supraconvergence of a finite difference scheme for solutions in Hs(0,L)","volume":"25","author":"Barbeiro","year":"2005","journal-title":"IMA J. Numer. Anal."},{"year":"2010","series-title":"Numerical Relativity: Solving Einstein's Equations on the Computer","author":"Baumgarte","key":"10.1016\/j.camwa.2024.08.016_br0050"},{"key":"10.1016\/j.camwa.2024.08.016_br0060","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75934-0","article-title":"The Mathematical Theory of Finite Element Methods","author":"Brenner","year":"2008"},{"key":"10.1016\/j.camwa.2024.08.016_br0070","doi-asserted-by":"crossref","first-page":"35","DOI":"10.21314\/JCF.2004.117","article-title":"A stochastic mesh method for pricing high-dimensional American options","volume":"7","author":"Broadie","year":"2004","journal-title":"J. Comput. Finance"},{"year":"1995","series-title":"High Accuracy Analysis of the Finite Element Method","author":"Chen","key":"10.1016\/j.camwa.2024.08.016_br0080"},{"year":"1978","series-title":"The Finite Element Method for Elliptic Equations","author":"Ciarlet","key":"10.1016\/j.camwa.2024.08.016_br0090"},{"issue":"4","key":"10.1016\/j.camwa.2024.08.016_br0100","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/j.chaos.2004.10.001","article-title":"Deriving the essential features of the standard model from the general theory of relativity","volume":"24","author":"El Naschie","year":"2005","journal-title":"Chaos Solitons Fractals"},{"year":"2013","series-title":"Theory and Practice of Finite Elements, vol. 159","author":"Ern","key":"10.1016\/j.camwa.2024.08.016_br0110"},{"key":"10.1016\/j.camwa.2024.08.016_br0120","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s11075-020-00892-y","article-title":"Superconvergence in H1-norm of a difference finite element method for the heat equation in a 3D spatial domain with almost-uniform mesh","volume":"86","author":"Feng","year":"2021","journal-title":"Numer. Algorithms"},{"issue":"1","key":"10.1016\/j.camwa.2024.08.016_br0130","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/21M1450872","article-title":"Difference finite element method for the 3D steady Navier\u2013Stokes equations","volume":"61","author":"Feng","year":"2023","journal-title":"SIAM J. Numer. Anal."},{"issue":"2\u20134","key":"10.1016\/j.camwa.2024.08.016_br0140","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/S0168-9274(98)00048-8","article-title":"On the supraconvergence of elliptic finite difference schemes","volume":"28","author":"Ferreira","year":"1998","journal-title":"Appl. Numer. Math."},{"issue":"312","key":"10.1016\/j.camwa.2024.08.016_br0150","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1090\/mcom\/3266","article-title":"H1-superconvergence of a difference finite element method based on the P1\u2212P1-conforming element on non-uniform meshes for the 3D Poisson equation","volume":"87","author":"He","year":"2018","journal-title":"Math. Comput."},{"issue":"2","key":"10.1016\/j.camwa.2024.08.016_br0160","doi-asserted-by":"crossref","first-page":"154","DOI":"10.4208\/eajam.180313.300513a","article-title":"H1 stability and convergence of the FE, FV and FD methods for an elliptic equation","volume":"3","author":"He","year":"2013","journal-title":"East Asian J. Appl. Math."},{"issue":"4","key":"10.1016\/j.camwa.2024.08.016_br0170","first-page":"642","article-title":"Laplace transformation method for the Black-Scholes equation","volume":"6","author":"Lee","year":"2009","journal-title":"Int. J. Numer. Anal. Model."},{"year":"2007","series-title":"Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems","author":"LeVeque","key":"10.1016\/j.camwa.2024.08.016_br0180"},{"issue":"2","key":"10.1016\/j.camwa.2024.08.016_br0190","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1137\/15M1013912","article-title":"Finite element pointwise results on convex polyhedral domains","volume":"54","author":"Leykekhman","year":"2016","journal-title":"SIAM J. Numer. Anal."},{"year":"2006","series-title":"Finite Element Methods and Their Applications","author":"Li","key":"10.1016\/j.camwa.2024.08.016_br0200"},{"year":"1996","series-title":"Construction and Analysis of Highly Efficient Finite Element","author":"Lin","key":"10.1016\/j.camwa.2024.08.016_br0210"},{"issue":"4","key":"10.1016\/j.camwa.2024.08.016_br0220","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1137\/0728056","article-title":"Ritz\u2013Volterra projections to finite-element spaces and applications to integrodifferential and related equations","volume":"28","author":"Lin","year":"1991","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.camwa.2024.08.016_br0230","article-title":"A difference finite element method based on three different discretized elements for the 4D Poisson equation","author":"Liu","year":"2024","journal-title":"East Asian J. Appl. Math."},{"issue":"2","key":"10.1016\/j.camwa.2024.08.016_br0240","doi-asserted-by":"crossref","first-page":"494","DOI":"10.4208\/nmtma.OA-2023-0122","article-title":"Stability and convergence of the integral-averaged interpolation operator based on Q1-element in Rn","volume":"17","author":"Liu","year":"2024","journal-title":"Numer. Math., Theory Methods Appl."},{"issue":"3","key":"10.1016\/j.camwa.2024.08.016_br0250","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1007\/s10915-022-01928-2","article-title":"A stabilized difference finite element method for the 3D steady incompressible Navier-Stokes equations","volume":"92","author":"Lu","year":"2022","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.camwa.2024.08.016_br0260","article-title":"A stabilized difference finite element method for the 3D steady Stokes equations","volume":"430","author":"Lu","year":"2022","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"10.1016\/j.camwa.2024.08.016_br0270","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1006\/jcph.1997.5656","article-title":"An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology","volume":"133","author":"Mattiussi","year":"1997","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.camwa.2024.08.016_br0280","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1137\/S0036144503429121","article-title":"A simple mesh generator in Matlab","volume":"46","author":"Persson","year":"2004","journal-title":"SIAM Rev."},{"issue":"158","key":"10.1016\/j.camwa.2024.08.016_br0290","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1090\/S0025-5718-1982-0645661-4","article-title":"Some optimal error estimates for piecewise linear finite element approximations","volume":"38","author":"Rannacher","year":"1982","journal-title":"Math. Comput."},{"issue":"1","key":"10.1016\/j.camwa.2024.08.016_br0300","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1137\/060649616","article-title":"Efficient hierarchical approximation of high-dimensional option pricing problems","volume":"29","author":"Reisinger","year":"2007","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.camwa.2024.08.016_br0310","first-page":"35","article-title":"Finite element and finite difference methods for continuous flows","volume":"1","author":"Russell","year":"2014","journal-title":"Math. Reserv. Simul."},{"issue":"4","key":"10.1016\/j.camwa.2024.08.016_br0320","doi-asserted-by":"crossref","first-page":"2470","DOI":"10.1137\/120875570","article-title":"On the derivation of highest-order compact finite difference schemes for the one- and two-dimensional Poisson equation with Dirichlet boundary conditions","volume":"51","author":"Settle","year":"2013","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.camwa.2024.08.016_br0330","series-title":"2018 MATRIX Annals","first-page":"121","article-title":"P1\u2013nonconforming polyhedral finite elements in high dimensions","volume":"vol. 3","author":"Sheen","year":"2018"},{"key":"10.1016\/j.camwa.2024.08.016_br0340","article-title":"Numerical Partial Differential Equations: Finite Difference Methods","volume":"vol. 22","author":"Thomas","year":"2013"},{"key":"10.1016\/j.camwa.2024.08.016_br0350","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10915-012-9607-6","article-title":"A family of fourth-order and sixth-order compact difference schemes for the three-dimensional Poisson equation","volume":"54","author":"Zhai","year":"2013","journal-title":"J. Sci. Comput."}],"container-title":["Computers & Mathematics with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122124003717?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122124003717?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:49:35Z","timestamp":1732668575000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0898122124003717"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11]]},"references-count":35,"alternative-id":["S0898122124003717"],"URL":"https:\/\/doi.org\/10.1016\/j.camwa.2024.08.016","relation":{},"ISSN":["0898-1221"],"issn-type":[{"type":"print","value":"0898-1221"}],"subject":[],"published":{"date-parts":[[2024,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A difference finite element method based on the conforming P1(x,y)\u00d7Q1(z,s) element for the 4D Poisson equation","name":"articletitle","label":"Article Title"},{"value":"Computers & Mathematics with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.camwa.2024.08.016","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}