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A Finite Element Method For PDEs in Time-Dependent Domains Olshanskiy, Maxim
Description
In the talk we discuss a recently introduced finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in a triangulated computational domain and can overlap the time-independent background mesh in an arbitrary way. The numerical method is based on finite difference discretizations of time derivatives and a standard geometrically unfitted finite element method with an additional stabilization term in the spatial domain. The performance and analysis of the method rely on the fundamental extension result in Sobolev spaces for functions defined on bounded domains. Theoretical findings include a complete stability and error analysis, which accounts for discretization errors resulting from finite difference and finite element approximations as well as for geometric errors coming from a possible approximate recovery of the physical domain. We show numerical examples that illustrate the theory and demonstrate the practical efficiency of the method.
Item Metadata
Title |
A Finite Element Method For PDEs in Time-Dependent Domains
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-07-30T09:43
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Description |
In the talk we discuss a recently introduced finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in a triangulated computational domain and can
overlap the time-independent background mesh in an arbitrary way. The numerical method is based on finite difference discretizations of time derivatives and a standard geometrically unfitted finite element
method with an additional stabilization term in the spatial domain. The performance and analysis of the method rely on the fundamental extension result in Sobolev spaces for functions defined on bounded domains. Theoretical findings include a complete stability and error analysis, which accounts for discretization errors resulting from finite difference and finite element approximations as well as for geometric errors coming from a possible approximate recovery of the physical domain. We show numerical examples that
illustrate the theory and demonstrate the practical efficiency of the method.
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Extent |
34.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Houston
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Series | |
Date Available |
2019-03-16
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0376999
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International