Spectral element method for parabolic interface problems: Regularity estimates, stability theorem and error estimate

Khan, Arbaz and Upadhyay, Chandra Shekhar and Gerritsma, Marc (2017) Spectral element method for parabolic interface problems: Regularity estimates, stability theorem and error estimate. [MIMS Preprint]

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Abstract

In this paper, an $h/p$ spectral element method with least-square formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for non-homogeneous interface data. The differentiability estimates and the main stability estimate theorem, using non-conforming spectral element functions, are proven. Error estimates are derived for $h$ and $p$ versions of the proposed method.

Item Type: MIMS Preprint
Uncontrolled Keywords: Least-squares method, nonconforming, spectral element method, Linear parabolic interface problems, Sobolev spaces of different orders in space and time
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Arbaz Khan
Date Deposited: 16 Sep 2017
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2575

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