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Error estimate of the operator splitting L2-NIPG method for two-dimensional time-fractional diffusion equations.

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Τίτλος: Error estimate of the operator splitting L2-NIPG method for two-dimensional time-fractional diffusion equations.
Συγγραφείς: Maji, Sandip1,2 (AUTHOR) smaji@shu.edu.cn, Natesan, Srinivasan1 (AUTHOR) natesan@iitg.ac.in
Πηγή: Numerical Algorithms. Sep2026, Vol. 103 Issue 1, p389-407. 19p.
Θεματικοί όροι: *Galerkin methods, *Caputo fractional derivatives, *Approximation error, *Partial differential equations, *Stability (Mechanics), *Fick's laws of diffusion, *Iterative methods (Mathematics)
Περίληψη: This article proposes an alternating direction implicit type operator splitting discontinuous Galerkin finite element method to solve a class of two-dimensional time-fractional diffusion equations numerically. Here, the operator splitting method allows us to split the two-dimensional diffusion equation into two separate one-dimensional equations. In both one-dimensional problems, the time-fractional Caputo derivative is discretized over a uniform mesh using the well-known L2-discretization, and the non-symmetric interior penalty discontinuous Galerkin method is used for the discretization of spatial derivatives over a uniform mesh. Stability and error estimate of the proposed fully discrete scheme are addressed. Finally, we give a numerical experiment to validate the theoretical efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
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  – Url: https://dx.doi.org/doi:10.1007/s11075-025-02235-1
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  Label: Title
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  Data: Error estimate of the operator splitting L2-NIPG method for two-dimensional time-fractional diffusion equations.
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  Data: <searchLink fieldCode="AR" term="%22Maji%2C+Sandip%22">Maji, Sandip</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> smaji@shu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Natesan%2C+Srinivasan%22">Natesan, Srinivasan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> natesan@iitg.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22Numerical+Algorithms%22">Numerical Algorithms</searchLink>. Sep2026, Vol. 103 Issue 1, p389-407. 19p.
– Name: Subject
  Label: Subject Terms
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  Data: *<searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br />*<searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br />*<searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br />*<searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br />*<searchLink fieldCode="DE" term="%22Stability+%28Mechanics%29%22">Stability (Mechanics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Fick's+laws+of+diffusion%22">Fick's laws of diffusion</searchLink><br />*<searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This article proposes an alternating direction implicit type operator splitting discontinuous Galerkin finite element method to solve a class of two-dimensional time-fractional diffusion equations numerically. Here, the operator splitting method allows us to split the two-dimensional diffusion equation into two separate one-dimensional equations. In both one-dimensional problems, the time-fractional Caputo derivative is discretized over a uniform mesh using the well-known L2-discretization, and the non-symmetric interior penalty discontinuous Galerkin method is used for the discretization of spatial derivatives over a uniform mesh. Stability and error estimate of the proposed fully discrete scheme are addressed. Finally, we give a numerical experiment to validate the theoretical efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
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      – Type: doi
        Value: 10.1007/s11075-025-02235-1
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 19
        StartPage: 389
    Subjects:
      – SubjectFull: Galerkin methods
        Type: general
      – SubjectFull: Caputo fractional derivatives
        Type: general
      – SubjectFull: Approximation error
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Stability (Mechanics)
        Type: general
      – SubjectFull: Fick's laws of diffusion
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
    Titles:
      – TitleFull: Error estimate of the operator splitting L2-NIPG method for two-dimensional time-fractional diffusion equations.
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            NameFull: Maji, Sandip
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            NameFull: Natesan, Srinivasan
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          Dates:
            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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              Value: 103
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            – TitleFull: Numerical Algorithms
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