Exponentially accurate spectral element method for fourth order elliptic problems
In this paper, a fully non-conforming least-squares spectral element method for fourth order elliptic problems on smooth domains is presented. The proposed method works for a general fourth order elliptic operator with non-homogeneous data in two dimensions and gives exponentially accurate solutions...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2017
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| In: |
Journal of scientific computing
Year: 2016, Volume: 71, Issue: 1, Pages: 303-328 |
| ISSN: | 1573-7691 |
| DOI: | 10.1007/s10915-016-0300-z |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s10915-016-0300-z Verlag, Volltext: https://link.springer.com/article/10.1007/s10915-016-0300-z 
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| Author Notes: | Arbaz Khan, Akhlaq Husain |
| Summary: | In this paper, a fully non-conforming least-squares spectral element method for fourth order elliptic problems on smooth domains is presented. The proposed method works for a general fourth order elliptic operator with non-homogeneous data in two dimensions and gives exponentially accurate solutions. We derive differentiability estimates and prove our main stability estimate theorem using a non-conforming spectral element method. We then formulate a numerical scheme using a block diagonal preconditioner. Error estimates are also proven for the proposed method. We provide the computational complexity of our method and present results of numerical simulations that have been performed to validate the theory. |
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| Item Description: | Published online: 04 October 2016 Gesehen am 16.08.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1573-7691 |
| DOI: | 10.1007/s10915-016-0300-z |