{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T22:07:03Z","timestamp":1771884423504,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,2,9]],"date-time":"2017-02-09T00:00:00Z","timestamp":1486598400000},"content-version":"unspecified","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":["11426090"],"award-info":[{"award-number":["11426090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2017,11]]},"DOI":"10.1007\/s11075-017-0277-1","type":"journal-article","created":{"date-parts":[[2017,2,8]],"date-time":"2017-02-08T23:16:26Z","timestamp":1486595786000},"page":"695-707","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Stability and convergence of a fully discrete local discontinuous Galerkin method for multi-term time fractional diffusion equations"],"prefix":"10.1007","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1688-7032","authenticated-orcid":false,"given":"Leilei","family":"Wei","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,2,9]]},"reference":[{"issue":"12","key":"277_CR1","first-page":"3293","volume":"28","author":"EE Adams","year":"1992","unstructured":"Adams, E.E., Gelhar, L.W.: Field study of dispersion in a heterogeneous aquifer: 2. Spatial moments analysis, Water Res. Research 28(12), 3293\u20133307 (1992)","journal-title":"Research"},{"key":"277_CR2","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1016\/j.jcp.2014.10.060","volume":"281","author":"AH Bhrawy","year":"2015","unstructured":"Bhrawy, A.H., Zaky, M.A.: A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations. J. Comput. Phys. 281, 876\u2013895 (2015)","journal-title":"J. Comput. Phys."},{"key":"277_CR3","doi-asserted-by":"crossref","first-page":"1540001","DOI":"10.1142\/S1793962315400012","volume":"6","author":"W Bu","year":"2015","unstructured":"Bu, W., Liu, X., Tang, Y., Yang, J.: Finite element multigrid method for multi-term time fractional advection diffusion equations. Int. J. Model. Simul. Sci. Comput. 6, 1540001 (2015)","journal-title":"Int. J. Model. Simul. Sci. Comput."},{"key":"277_CR4","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1515\/fca-2015-0043","volume":"18","author":"X Ding","year":"2015","unstructured":"Ding, X., Nieto, J.: Analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain. Fract. Calc. Appl. Anal. 18, 697\u2013716 (2015)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"277_CR5","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/S0377-0427(02)00558-7","volume":"148","author":"JT Edwards","year":"2002","unstructured":"Edwards, J.T., Neville, J.F., Simpson, A.C.: The numerical solution of linear multi-term fractional differential equations: systems of equations. J. Comp. Anal. Appl. 148, 401\u2013418 (2002)","journal-title":"J. Comp. Anal. Appl."},{"key":"277_CR6","first-page":"243","volume":"6","author":"K Diethelm","year":"2004","unstructured":"Diethelm, K., Luchko, Y.: Numerical solution of linear multi-term differential equations of fractional order. J. Comp. Anal. Appl. 6, 243\u2013263 (2004)","journal-title":"J. Comp. Anal. Appl."},{"key":"277_CR7","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1016\/j.jmaa.2011.12.055","volume":"389","author":"H Jiang","year":"2012","unstructured":"Jiang, H., Liu, F., Turner, I., Burrage, K.: Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. J. Math. Anal. Appl. 389, 1117\u20131127 (2012)","journal-title":"J. Math. Anal. Appl."},{"key":"277_CR8","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1016\/j.jcp.2014.10.051","volume":"281","author":"B Jin","year":"2015","unstructured":"Jin, B., Liu, Y., Zhou, Z.: The Galerkin finite element method for a multi-term time-fractional diffusion equation. J. Comput. Phys. 281, 825\u2013843 (2015)","journal-title":"J. Comput. Phys."},{"key":"277_CR9","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1002\/zamm.200900252","volume":"89","author":"JT Katsikadelis","year":"2009","unstructured":"Katsikadelis, J.T.: Numerical solution of multi-term fractional differential equations. Z. Angew. Math. Mech. 89, 593\u2013608 (2009)","journal-title":"Z. Angew. Math. Mech."},{"issue":"5","key":"277_CR10","doi-asserted-by":"crossref","first-page":"2861","DOI":"10.1121\/1.2977669","volume":"124","author":"JF Kelly","year":"2008","unstructured":"Kelly, J.F., McGough, R.J., Meerschaert, M.M.: Analytical time-domain Greens functions for power-law media. J. Acoust. Soc. Am. 124(5), 2861\u20132872 (2008)","journal-title":"J. Acoust. Soc. Am."},{"issue":"1","key":"277_CR11","doi-asserted-by":"crossref","first-page":"9","DOI":"10.2478\/s13540-013-0002-2","volume":"16","author":"F Liu","year":"2013","unstructured":"Liu, F., Meerschaert, M.M., McGough, R.J., Zhuang, P., Liu, X.: Numerical methods for solving the multi-term time-fractional wave-diffusion equation,. Frac. Cal. Appl. Anal. 16(1), 9\u201325 (2013)","journal-title":"Frac. Cal. Appl. Anal."},{"key":"277_CR12","doi-asserted-by":"crossref","first-page":"9","DOI":"10.2478\/s13540-013-0002-2","volume":"16","author":"F Liu","year":"2013","unstructured":"Liu, F., Meerschaert, M.M., McGough, R., Zhuang, P., Liu, Q.: Numerical methods for solving the multi-term time fractional wave equations. Fract. Calc. Appl. Anal. 16, 9\u201325 (2013)","journal-title":"Fract. Calc. Appl. Anal."},{"issue":"2","key":"277_CR13","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1103\/PhysRevE.58.1621","volume":"58","author":"R Metzler","year":"1998","unstructured":"Metzler, R., Klafter, J., Sokolov, I.M.: Anomalous transport in external fields: continuous time random walks and fractional diffusion equations extended. Phys. Rev. E 58(2), 1621\u20131633 (1998)","journal-title":"Phys. Rev. E"},{"key":"277_CR14","unstructured":"Podlubny, I.: Fractional Differential Equations, vol. 198, Academic Press, San Diego, USA (1999)"},{"key":"277_CR15","first-page":"242","volume":"4","author":"J Ren","year":"2014","unstructured":"Ren, J., Sun, Z.: Efficient and stable numerical methods for multi-term time-fractional sub-diffusion equations, East Asian. J. Appl. Math. 4, 242\u2013266 (2014)","journal-title":"J. Appl. Math."},{"key":"277_CR16","first-page":"1","volume":"5","author":"J Ren","year":"2015","unstructured":"Ren, J., Sun, Z.: Efficient numerical solution of multi-term time-fractional diffusion-wave equation, East Asian. J. Appl. Math. 5, 1\u201328 (2015)","journal-title":"J. Appl. Math."},{"issue":"10","key":"277_CR17","first-page":"129","volume":"39","author":"R Schumer","year":"2003","unstructured":"Schumer, R., Benson, D.A., Meerschaert, M.M., Baeumer, B.: Fractal mobile\/immobile solute transport, Water Res. Research 39(10), 129\u2013613 (2003)","journal-title":"Research"},{"key":"277_CR18","doi-asserted-by":"crossref","first-page":"2943","DOI":"10.1016\/j.mcm.2011.07.016","volume":"54","author":"L Shao","year":"2011","unstructured":"Shao, L., Feng, X., He, Y.: The local discontinuous Galerkin finite element method for Burger\u2019s equation. Math. Comput. Modelling 54, 2943\u20132954 (2011)","journal-title":"Math. Comput. Modelling"},{"key":"277_CR19","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1016\/j.apm.2013.07.040","volume":"38","author":"LL Wei","year":"2014","unstructured":"Wei, L.L., He, Y.N.: Analysis of a fully discrete local discontinuous Galerkin method for time-fractional fourth-order problems. Appl. Math. Model. 38, 1511\u20131522 (2014)","journal-title":"Appl. Math. Model."},{"key":"277_CR20","first-page":"821","volume":"5","author":"Y Xia","year":"2009","unstructured":"Xia, Y., Xu Y., Shu, C.-W.: Application of the local discontinuous Galerkin method for the Allen-Cahn\/Cahn-Hilliard system. Commun. Comput. Phys. 5, 821\u2013835 (2009)","journal-title":"Commun. Comput. Phys."},{"key":"277_CR21","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1137\/070679764","volume":"46","author":"Y Xu","year":"2008","unstructured":"Xu, Y., Shu, C.-W.: Local discontinuous Galerkin method for the Camassa-Holm equation. SIAM J. Numer. Anal. 46, 1998\u20132021 (2008)","journal-title":"SIAM J. Numer. Anal."},{"key":"277_CR22","first-page":"857205","volume":"2013","author":"J Zhao","year":"2013","unstructured":"Zhao, J., Xiao, J., Xu, Y.: Stability and convergence of an effective finite element method for multi-term fractional partial differential equations. Abstr. Appl. Anal. 2013, 857205 (2013)","journal-title":"Abstr. Appl. Anal."},{"key":"277_CR23","doi-asserted-by":"publisher","unstructured":"Zhao, Y., Zhang, Y., Liu, F., Turner, I., Tang, Y., Anh, V.: Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations. Comput. Math. Appl. doi: 10.1016\/j.camwa.2016.05.005 (2016)","DOI":"10.1016\/j.camwa.2016.05.005"},{"key":"277_CR24","doi-asserted-by":"crossref","first-page":"49704985","DOI":"10.1016\/j.apm.2015.12.011","volume":"40","author":"M Zheng","year":"2016","unstructured":"Zheng, M., Liu, F., Anh, V., Turner, I.: A high-order spectral method for the multi-term time-fractional diffusion equations. Appl. Math. Model. 40, 49704985 (2016)","journal-title":"Appl. Math. Model."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0277-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0277-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0277-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,23]],"date-time":"2022-07-23T21:16:13Z","timestamp":1658610973000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0277-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,9]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["277"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0277-1","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,9]]}}}