Spectral element method for three dimensional elliptic problems with smooth interfaces
In this paper we propose a least-squares spectral element method for three dimensional elliptic interface problems. The differentiability estimates and the main stability theorem, using non-conforming spectral element functions, are proven. The proposed method is free from any kind of first order re...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2017
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| In: |
Computer methods in applied mechanics and engineering
Year: 2016, Volume: 315, Pages: 522-549 |
| ISSN: | 1879-2138 |
| DOI: | 10.1016/j.cma.2016.11.003 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1016/j.cma.2016.11.003 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0045782516308271 
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| Author Notes: | Arbaz Khan, Akhlaq Husain, Subhashree Mohapatra, Chandra Shekhar Upadhyay |
| Summary: | In this paper we propose a least-squares spectral element method for three dimensional elliptic interface problems. The differentiability estimates and the main stability theorem, using non-conforming spectral element functions, are proven. The proposed method is free from any kind of first order reformulation. A suitable preconditioner is constructed with help of the regularity estimate and proposed stability estimates which is used to control the condition number. We show that these preconditioners are spectrally equivalent to the quadratic forms by which we approximate them. We obtain the error estimates which show the exponential accuracy of the method. Numerical results are obtained for both straight and curved interfaces to show the efficiency of the proposed method. |
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| Item Description: | Available online 14 November 2016 Gesehen am 16.08.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1879-2138 |
| DOI: | 10.1016/j.cma.2016.11.003 |