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Transmission conditions with constraints in finite element domain decomposition methods for flow problems.

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Title: Transmission conditions with constraints in finite element domain decomposition methods for flow problems.
Authors: Houzeaux, G.1, Codina, R.2
Source: Communications in Numerical Methods in Engineering. Mar2001, Vol. 17 Issue 3, p179-190. 12p. 10 Diagrams, 2 Charts.
Subjects: Finite element method, Numerical analysis, Stokes equations, Partial differential equations
Abstract: This work presents a conservative scheme for iteration-by-subdomain domain decomposition (DD) strategies applied to the finite element solution of flow problems. The DD algorithm is based on the iterative update of the boundary conditions on the interfaces between the subregions, the so-called transmission conditions. The transmission conditions involve the essential and natural boundary conditions of the weak form of the problem, and should ensure strong continuity of the velocity and weak continuity of the traction. As a first approach, the transmission conditions are interpolated using the classical Lagrange interpolation functions. Conservation problems might arise when two adjacent subdomains have a sensibly different mesh spacing. In order to conserve any desired quantity of interest, an interface constraining is introduced: continuity of the transmission conditions are constrained under a scalar conservation equation. An example of mass conservation illustrates the algorithm. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Transmission conditions with constraints in finite element domain decomposition methods for flow problems.
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  Data: <searchLink fieldCode="JN" term="%22Communications+in+Numerical+Methods+in+Engineering%22">Communications in Numerical Methods in Engineering</searchLink>. Mar2001, Vol. 17 Issue 3, p179-190. 12p. 10 Diagrams, 2 Charts.
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  Data: This work presents a conservative scheme for iteration-by-subdomain domain decomposition (DD) strategies applied to the finite element solution of flow problems. The DD algorithm is based on the iterative update of the boundary conditions on the interfaces between the subregions, the so-called transmission conditions. The transmission conditions involve the essential and natural boundary conditions of the weak form of the problem, and should ensure strong continuity of the velocity and weak continuity of the traction. As a first approach, the transmission conditions are interpolated using the classical Lagrange interpolation functions. Conservation problems might arise when two adjacent subdomains have a sensibly different mesh spacing. In order to conserve any desired quantity of interest, an interface constraining is introduced: continuity of the transmission conditions are constrained under a scalar conservation equation. An example of mass conservation illustrates the algorithm. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
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  Label:
  Group: Ab
  Data: <i>Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/cnm.397
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        Text: English
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      – SubjectFull: Stokes equations
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      – TitleFull: Transmission conditions with constraints in finite element domain decomposition methods for flow problems.
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              Text: Mar2001
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