{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T23:47:42Z","timestamp":1777420062444,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,1,18]],"date-time":"2016-01-18T00:00:00Z","timestamp":1453075200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11271173"],"award-info":[{"award-number":["11271173"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471150"],"award-info":[{"award-number":["11471150"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"CAPES and CNPq in Brazil"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2016,8]]},"DOI":"10.1007\/s10915-015-0160-y","type":"journal-article","created":{"date-parts":[[2016,1,18]],"date-time":"2016-01-18T06:33:33Z","timestamp":1453098813000},"page":"826-847","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A Hybridized Discontinuous Galerkin Method for 2D Fractional Convection\u2013Diffusion Equations"],"prefix":"10.1007","volume":"68","author":[{"given":"Shuqin","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinyun","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weihua","family":"Deng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yujiang","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,1,18]]},"reference":[{"issue":"6","key":"160_CR1","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1029\/2000WR900032","volume":"36","author":"DA Benson","year":"2000","unstructured":"Benson, D.A., Wheatcraft, S.W., Meerschaert, M.M.: The fractional-order governing equation of L\u00e9vy motion. Water Resour. Res. 36(6), 1413\u20131423 (2000)","journal-title":"Water Resour. Res."},{"issue":"12","key":"160_CR2","doi-asserted-by":"crossref","first-page":"5096","DOI":"10.1063\/1.1416180","volume":"8","author":"BA Carreras","year":"2001","unstructured":"Carreras, B.A., Lynch, V.E., Zaslavsky, G.M.: Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model. Phys. Plasmas 8(12), 5096\u20135103 (2001)","journal-title":"Phys. Plasmas"},{"issue":"5","key":"160_CR3","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.1137\/S0036142900371003","volume":"38","author":"P Castilo","year":"2000","unstructured":"Castilo, P., Cockburn, B., Perugia, I., S\u00f6tzau, D.: An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. SIAM J. Numer. Anal. 38(5), 1676\u20131706 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"160_CR4","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1016\/S0045-7825(01)00411-X","volume":"191","author":"ZX Chen","year":"2002","unstructured":"Chen, Z.X.: Characteristic mixed discontinuous finite element methods for advection-dominated diffusion problems. Comput. Methods Appl. Mech. Eng. 191, 2509\u20132538 (2002)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"160_CR5","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1137\/S003614290037068X","volume":"40","author":"ZX Chen","year":"2003","unstructured":"Chen, Z.X., Ewing, R.E., Jiang, Q.Y., Spagnuolo, M.: Error analysis for characteristic-based methods for degenerate parabolic problems. SIAM J. Numer. Anal. 40, 1491\u20131515 (2003)","journal-title":"SIAM J. Numer. Anal."},{"issue":"13","key":"160_CR6","doi-asserted-by":"crossref","first-page":"3244","DOI":"10.1016\/j.apm.2013.11.043","volume":"38","author":"MH Chen","year":"2014","unstructured":"Chen, M.H., Deng, W.H.: A second-order numerical method for two-dimensional two-sided space fractional convection-diffusion equation. Appl. Math. Model. 38(13), 3244\u20133259 (2014)","journal-title":"Appl. Math. Model."},{"issue":"6","key":"160_CR7","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1137\/S0036142997316712","volume":"35","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convection\u2013diffusion systems. SIAM J. Numer. Anal. 35(6), 2440\u20132463 (1998)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"160_CR8","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1012873910884","volume":"16","author":"B Cockburn","year":"2001","unstructured":"Cockburn, B., Shu, C.-W.: Runge\u2013Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16(3), 173\u2013261 (2001)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"160_CR9","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s00211-014-0661-x","volume":"130","author":"B Cockburn","year":"2015","unstructured":"Cockburn, B., Mustapha, K.: A hybridizable discontinuous Galerkin method for fractional diffusion problems. Numer. Math. 130(2), 293\u2013314 (2015)","journal-title":"Numer. Math."},{"key":"160_CR10","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/j.cam.2013.06.001","volume":"255","author":"MR Cui","year":"2014","unstructured":"Cui, M.R.: A high-order compact exponential scheme for fractional convection\u2013diffusion equations. J. Comput. Appl. Math. 255, 404\u2013416 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"160_CR11","doi-asserted-by":"crossref","first-page":"1845","DOI":"10.1051\/m2an\/2013091","volume":"47","author":"WH Deng","year":"2013","unstructured":"Deng, W.H., Hesthaven, J.S.: Local discontinuous Galerkin methods for fractional diffusion equations. ESAIM Math. Model. Numer. Anal. 47, 1845\u20131864 (2013)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"5","key":"160_CR12","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1137\/0719063","volume":"19","author":"J Douglas Jr","year":"1982","unstructured":"Douglas Jr, J., Russell, T.F.: Numerical method for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19(5), 871\u2013885 (1982)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"160_CR13","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1002\/num.20112","volume":"22","author":"VJ Ervin","year":"2006","unstructured":"Ervin, V.J., Roop, J.P.: Variational formulation for the stational fractional advection dispersion equation. Numer. Methods Partial Differ. Equ. 22(3), 558\u2013576 (2006)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"160_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-72067-8","volume-title":"Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications","author":"JS Hesthaven","year":"2008","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer, New York (2008)"},{"issue":"3","key":"160_CR15","doi-asserted-by":"crossref","first-page":"333","DOI":"10.4208\/nmtma.2012.m1107","volume":"5","author":"X Ji","year":"2012","unstructured":"Ji, X., Tang, H.Z.: High-order accurate Runge\u2013Kutta (local) discontinuous Galerkin methods for one- and two-dimensional fractional diffusion equations. Numer. Math. Theor. Methods Appl. 5(3), 333\u2013358 (2012)","journal-title":"Numer. Math. Theor. Methods Appl."},{"key":"160_CR16","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1038\/35000537","volume":"403","author":"JW Kirchner","year":"2002","unstructured":"Kirchner, J.W., Feng, X.H., Neal, C.: Fractal stream chemistry and its implication for contaminant transport in catchments. Nature 403, 524\u2013526 (2002)","journal-title":"Nature"},{"key":"160_CR17","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1016\/j.jcp.2007.02.001","volume":"225","author":"Y Lin","year":"2007","unstructured":"Lin, Y., Xu, C.J.: Finite difference\/spectral approximations for the time-fractional diffusion equations. J. Comput. Phys. 225, 1533\u20131552 (2007)","journal-title":"J. Comput. Phys."},{"key":"160_CR18","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.amc.2006.08.162","volume":"191","author":"F Liu","year":"2007","unstructured":"Liu, F., Zhuang, P., Anh, V., Turner, I., Burrage, K.: Stability and convergence of the difference methods for the space\u2013time fractional advection\u2013diffusion equation. Appl. Math. Comput. 191, 12\u201320 (2007)","journal-title":"Appl. Math. Comput."},{"key":"160_CR19","volume-title":"Fractional Calculus in Bioengineering","author":"RL Magin","year":"2006","unstructured":"Magin, R.L.: Fractional Calculus in Bioengineering. Begell House, Redding (2006)"},{"issue":"1","key":"160_CR20","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s11075-008-9258-8","volume":"52","author":"W Mclean","year":"2009","unstructured":"Mclean, W., Mustapha, K.: Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation. Numer. Algor. 52(1), 69\u201388 (2009)","journal-title":"Numer. Algor."},{"issue":"1","key":"160_CR21","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1137\/120880719","volume":"51","author":"W Mclean","year":"2013","unstructured":"Mclean, W., Mustapha, K.: Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations. SIAM J. Numer. Anal. 51(1), 491\u2013515 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"160_CR22","doi-asserted-by":"crossref","first-page":"A3039","DOI":"10.1137\/120870505","volume":"34","author":"W Mclean","year":"2012","unstructured":"Mclean, W.: Fast summation by interval clustering for an evolution equation with memory. SIAM J. Sci. Comput. 34(6), A3039\u2013A3056 (2012)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"160_CR23","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s11075-010-9379-8","volume":"56","author":"K Mustapha","year":"2001","unstructured":"Mustapha, K., Mclean, W.: Piece-linear, discontinuous Galerkin method for a fractional diffusion equation. Numer. Algor. 56(2), 159\u2013184 (2001)","journal-title":"Numer. Algor."},{"issue":"3","key":"160_CR24","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/s00211-014-0669-2","volume":"130","author":"K Mustapha","year":"2015","unstructured":"Mustapha, K.: Time-stepping discontinuous Galerkin methods for fractional diffusion problems. Numer. Math. 130(3), 497\u2013516 (2015)","journal-title":"Numer. Math."},{"key":"160_CR25","volume-title":"The Fractional Calculus","author":"KB Oldham","year":"1974","unstructured":"Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)"},{"key":"160_CR26","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1016\/j.jcp.2015.06.022","volume":"298","author":"LL Qiu","year":"2015","unstructured":"Qiu, L.L., Deng, W.H., Hesthaven, J.S.: Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangualr meshes. J. Comput. Phys. 298, 678\u2013694 (2015)","journal-title":"J. Comput. Phys."},{"key":"160_CR27","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717440","volume-title":"Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation","author":"B Rivi\u00e8re","year":"2008","unstructured":"Rivi\u00e8re, B.: Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation. SIAM, Philadelphia (2008)"},{"issue":"11","key":"160_CR28","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1103\/PhysRevLett.58.1100","volume":"58","author":"MF Shlesinger","year":"1987","unstructured":"Shlesinger, M.F., West, B.J., Klafter, J.: L\u00e9vy dynamics of enhanced diffusion: application to turbulence. Phys. Rev. Lett. 58(11), 1100\u20131103 (1987)","journal-title":"Phys. Rev. Lett."},{"key":"160_CR29","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.camwa.2014.05.016","volume":"68","author":"ZB Wang","year":"2014","unstructured":"Wang, Z.B., Vong, S.W.: A high-order exponential ADI scheme for two dimensional time fractional convection\u2013diffusion equations. Comput. Math. Appl. 68, 185\u2013196 (2014)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"160_CR30","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1137\/130918174","volume":"52","author":"Q Xu","year":"2014","unstructured":"Xu, Q., Hesthaven, J.S.: Discontinuous Galerkin method for fractional convection\u2013diffusion equations. SIAM J. Numer. Anal. 52(1), 405\u2013423 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"160_CR31","doi-asserted-by":"crossref","unstructured":"Zhai, S.Y., Feng, X.L., He, Y.N.: An unconditionally stable compact ADI method for three-dimensional time-fractional convection\u2013diffusion equations. J. Comput. Phys. 269, 138\u2013155 (2014)","DOI":"10.1016\/j.jcp.2014.03.020"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0160-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-015-0160-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0160-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T21:07:12Z","timestamp":1718312832000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-015-0160-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,18]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["160"],"URL":"https:\/\/doi.org\/10.1007\/s10915-015-0160-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,18]]}}}