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Symmetric stabilized FEM for time-fractional convection–diffusion–reaction equations

Author

Listed:
  • Ahmed, Naveed
  • Karaa, Samir
  • Jha, Abhinav

Abstract

This paper presents a stabilized finite element method for solving time-fractional convection–diffusion–reaction equations. The approach combines a symmetric stabilization technique in space with a time-stepping method based on a convolution quadrature generated by the backward method and an L1 finite difference scheme. The stability of the semi-discrete problem is analyzed, and optimal error estimates are initially derived under high regularity assumptions on the initial condition and the solution. To relax these regularity requirements, a refined energy technique is employed, extending the error analysis to nonsmooth initial conditions and increasing the method’s applicability. Numerical simulations are presented, confirming the effectiveness and accuracy of the proposed scheme.

Suggested Citation

  • Ahmed, Naveed & Karaa, Samir & Jha, Abhinav, 2026. "Symmetric stabilized FEM for time-fractional convection–diffusion–reaction equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 245(C), pages 685-697.
    • Handle: RePEc:eee:matcom:v:245:y:2026:i:c:p:685-697
    DOI: 10.1016/j.matcom.2026.02.003
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    References listed on IDEAS

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    1. Roland Becker & Malte Braack, 2004. "A Two-Level Stabilization Scheme for the Navier-Stokes Equations," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 123-130, Springer.
    2. Chang, Ailian & Sun, HongGuang & Zheng, Chunmiao & Lu, Bingqing & Lu, Chengpeng & Ma, Rui & Zhang, Yong, 2018. "A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 356-369.
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    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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