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

Muhammad Arshad*, Rukhsana Jabeen, Suliman Khan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)127-150
Number of pages24
JournalMathematics and Computers in Simulation
Volume198
DOIs
StatePublished - Aug 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 International Association for Mathematics and Computers in Simulation (IMACS)

Keywords

  • Domain decomposition
  • Error estimates
  • Expanded mixed method
  • Fully discrete
  • Multiscale method
  • Parabolic equations
  • Semi discrete

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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