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A multiscale domain decomposition approach for parabolic equations using expanded mixed method

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  • Arshad, Muhammad
  • Jabeen, Rukhsana
  • Khan, Suliman

Abstract

We study the multiscale mortar expanded mixed method for second order parabolic partial differential equations. This technique involves non-overlapping domain decomposition which restrict a large problem into smaller pieces. Each block in the domain decomposition is discretized by expanded mixed method. The flux continuity is ensured by constructing a finite element space on the interface between subdomains. A pressure variable is introduced on the interfaces which play the role of Dirichlet boundary condition for each subdomain internal boundary. We demonstrate the unique solvability of discrete problem. We considered both continuous time and discrete time formulation and established a priori error estimates for local subdomain approximations. We derived the optimal order convergence for the appropriate choice of mortar space. An error estimate for mortar pressure variable is also provided. The numerical experiments are performed to show the accuracy and effectiveness of method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:127-150
    DOI: 10.1016/j.matcom.2022.02.010
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    References listed on IDEAS

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    1. Arshad, Muhammad & Park, Eun-Jae, 2020. "Multiscale mortar expanded mixed discretization of nonlinear elliptic problems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    2. 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.
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    1. 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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