Multiblock Mortar Mixed Approach for Second Order Parabolic Problems

Muhammad Arshad, Madiha Sana and Muhammad Mustahsan
Additional contact information
Muhammad Arshad: Department of Mathematics, Abbottabad University of Science and Technology, 22500 Abbottabad, Pakistan
Madiha Sana: Department of Mathematics, The Islamia University of Bahawalpur, 63100 Bahawalpur, Pakistan
Muhammad Mustahsan: Department of Mathematics, The Islamia University of Bahawalpur, 63100 Bahawalpur, Pakistan

Mathematics, 2019, vol. 7, issue 4, 1-18

Abstract: In this paper, the multiblock mortar mixed approximation of second order parabolic partial differential equations is considered. In this method, the simulation domain is decomposed into the non-overlapping subdomains (blocks), and a physically-meaningful boundary condition is set on the mortar interface between the blocks. The governing equations hold locally on each subdomain region. The local problems on blocks are coupled by introducing a special approximation space on the interfaces of neighboring subdomains. Each block is locally covered by an independent grid and the standard mixed finite element method is applied to solve the local problem. The unique solvability of the discrete problem is shown, and optimal order convergence rates are established for the approximate velocity and pressure on the subdomain. Furthermore, an error estimate for the interface pressure in mortar space is presented. The numerical experiments are presented to validate the efficiency of the method.

Keywords: parabolic problem; domain decomposition; semidiscrete; multiblock; mortar mixed method; elliptic projection; error estimates; interface error (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/4/325/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/4/325/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:4:p:325-:d:219329

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().