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      A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations

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          Abstract

          A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple ( L 2(Ω) 2) space replacing the complex H(div; Ω) space. Some a priori error estimates in L 2-norm for the scalar unknown u and in ( L 2) 2-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H 1-norm for the scalar unknown u.

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          Finite difference approximations for fractional advection–dispersion flow equations

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            Finite difference/spectral approximations for the time-fractional diffusion equation

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              Finite difference approximations for two-sided space-fractional partial differential equations

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                Author and article information

                Journal
                ScientificWorldJournal
                ScientificWorldJournal
                TSWJ
                The Scientific World Journal
                Hindawi Publishing Corporation
                1537-744X
                2014
                9 March 2014
                : 2014
                : 141467
                Affiliations
                School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
                Author notes

                Academic Editors: Q. Liu, F. Soleymani, and G. Tsiatas

                Author information
                http://orcid.org/0000-0001-8218-0196
                Article
                10.1155/2014/141467
                3967637
                24737957
                842a94b0-f767-4fb5-a157-9137f7c31f5d
                Copyright © 2014 Yang Liu et al.

                This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 4 December 2013
                : 16 January 2014
                Funding
                Funded by: http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China
                Award ID: 11301258
                Funded by: http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China
                Award ID: 11361035
                Categories
                Research Article

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