Conforming and Nonconforming Finite Element Methods for Biharmonic Inverse Source Problem Article Swipe
Devika Shylaja
,
M. Thamban Nair
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2106.07357
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2106.07357
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and nonconforming finite element methods (FEMs). The inverse problem is analysed through the forward problem. Error estimate for the forward solution is derived in an abstract set-up that applies to conforming and Morley nonconforming FEMs. Since the inverse problem is ill-posed, Tikhonov regularisation is considered to obtain a stable approximate solution. Error estimate is established for the regularised solution for different regularisation schemes. Numerical results that confirm the theoretical results are also presented.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2106.07357
- https://arxiv.org/pdf/2106.07357
- OA Status
- green
- References
- 6
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3166284408
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- OpenAlex ID
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https://openalex.org/W3166284408Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2106.07357Digital Object Identifier
- Title
-
Conforming and Nonconforming Finite Element Methods for Biharmonic Inverse Source ProblemWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-06-14Full publication date if available
- Authors
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Devika Shylaja, M. Thamban NairList of authors in order
- Landing page
-
https://arxiv.org/abs/2106.07357Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2106.07357Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2106.07357Direct OA link when available
- Concepts
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Biharmonic equation, Tikhonov regularization, Finite element method, Inverse problem, Mathematics, Inverse, Applied mathematics, Set (abstract data type), Mathematical analysis, Mathematical optimization, Computer science, Geometry, Physics, Boundary value problem, Programming language, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- References (count)
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6Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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