IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v323y2018icp31-42.html
   My bibliography  Save this article

Superconvergence analysis of finite element method for time-fractional Thermistor problem

Author

Listed:
  • Shi, Dongyang
  • Yang, Huaijun

Abstract

In this paper, the superclose and superconvergence analysis of the nonlinear time-fractional thermistor problem are investigated by bilinear finite element method (FEM) for a fully-discrete scheme, in which the Caputo derivative is approximated by the classical L1 method. By dealing with the error estimates in the spatial direction rigorously, which are one order higher than the traditional FEMs, the superclose estimates in H1-norm are obtained for the corresponding variables based on the special properties of this element together with mean value technique. Subsequently, the global superconvergence results are derived by employing the interpolation postprocessing approach. Finally, a numerical experiment is carried out to confirm the theoretical analysis.

Suggested Citation

  • Shi, Dongyang & Yang, Huaijun, 2018. "Superconvergence analysis of finite element method for time-fractional Thermistor problem," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 31-42.
    • Handle: RePEc:eee:apmaco:v:323:y:2018:i:c:p:31-42
    DOI: 10.1016/j.amc.2017.11.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317308093
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.11.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    2. Shi, Dongyang & Liao, Xin & Wang, Lele, 2016. "Superconvergence analysis of conforming finite element method for nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 298-310.
    3. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yin, Baoli & Liu, Yang & Li, Hong, 2020. "A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    2. Shi, Xiangyu & Lu, Linzhang, 2020. "A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    3. Gao, Xinghua & Yin, Baoli & Li, Hong & Liu, Yang, 2021. "TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 117-137.
    4. Shi, Dongyang & Yang, Huaijun, 2019. "Superconvergence analysis of nonconforming FEM for nonlinear time-dependent thermistor problem," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 210-224.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marseguerra, Marzio & Zoia, Andrea, 2008. "Pre-asymptotic corrections to fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2668-2674.
    2. Zheng, Guang-Hui & Zhang, Quan-Guo, 2018. "Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 37-47.
    3. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    4. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
    5. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
    6. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    7. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    8. Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006. "Growth and allocation of resources in economics: The agent-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.
    9. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    10. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    11. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2022. "Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method," Mathematics, MDPI, vol. 10(12), pages 1-16, June.
    12. Hayashi, Katsuhiko & Kaizoji, Taisei & Pichl, Lukáš, 2007. "Correlation patterns of NIKKEI index constituents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 16-21.
    13. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2009. "Detrended fluctuation analysis of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 433-440.
    14. Enrico Scalas & Rudolf Gorenflo & Hugh Luckock & Francesco Mainardi & Maurizio Mantelli & Marco Raberto, 2004. "Anomalous waiting times in high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 695-702.
    15. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    16. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
    17. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    18. Berardi, Luca & Serva, Maurizio, 2005. "Time and foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 403-412.
    19. Masoliver, Jaume & Montero, Miquel & Perello, Josep & Weiss, George H., 2006. "The continuous time random walk formalism in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 577-598, December.
    20. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:323:y:2018:i:c:p:31-42. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.