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A new expanded mixed method for parabolic integro-differential equations

Author

Listed:
  • Liu, Yang
  • Fang, Zhichao
  • Li, Hong
  • He, Siriguleng
  • Gao, Wei

Abstract

A new expanded mixed scheme is studied and analyzed for linear parabolic integro-differential equations. The proposed method’s gradient belongs to the simple square integrable space replacing the classical H(div;Ω) space. The new expanded mixed projection is introduced, the existence and uniqueness of solution for semi-discrete scheme are proved and the fully discrete error estimates based on both backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L2 and H1-norm for the scalar unknown u and the error results in L2(Ω)-norm for its gradient λ, and its flux σ (the coefficients times the negative gradient) are derived. Finally, some numerical results are calculated to verify our theoretical analysis.

Suggested Citation

  • Liu, Yang & Fang, Zhichao & Li, Hong & He, Siriguleng & Gao, Wei, 2015. "A new expanded mixed method for parabolic integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 600-613.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:600-613
    DOI: 10.1016/j.amc.2015.02.081
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    Cited by:

    1. Arshad, Muhammad & Jabeen, Rukhsana & Khan, Suliman, 2022. "A multiscale domain decomposition approach for parabolic equations using expanded mixed method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 127-150.
    2. Arshad, Muhammad & Park, Eun-Jae, 2020. "Multiscale mortar expanded mixed discretization of nonlinear elliptic problems," Applied Mathematics and Computation, Elsevier, vol. 371(C).

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