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Open AccessArticle

Multiblock Mortar Mixed Approach for Second Order Parabolic Problems

1
Department of Mathematics, Abbottabad University of Science and Technology, 22500 Abbottabad, Pakistan
2
Department of Mathematics, The Islamia University of Bahawalpur, 63100 Bahawalpur, Pakistan
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(4), 325; https://doi.org/10.3390/math7040325
Received: 17 February 2019 / Revised: 17 March 2019 / Accepted: 18 March 2019 / Published: 2 April 2019
(This article belongs to the Special Issue Finite Element Analysis)
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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. View Full-Text
Keywords: parabolic problem; domain decomposition; semidiscrete; multiblock; mortar mixed method; elliptic projection; error estimates; interface error parabolic problem; domain decomposition; semidiscrete; multiblock; mortar mixed method; elliptic projection; error estimates; interface error
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Arshad, M.; Sana, M.; Mustahsan, M. Multiblock Mortar Mixed Approach for Second Order Parabolic Problems. Mathematics 2019, 7, 325.

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