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Flux-mortar mixed f...
Flux-mortar mixed finite element methods on nonmatching grids
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- Boon, Wietse M. (författare)
- KTH,Numerisk analys, NA
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- Glaeser, Dennis (författare)
- Univ Stuttgart, Inst Modelling Hydraul & Environm Syst, D-70569 Stuttgart, Germany.
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- Helmig, Rainer (författare)
- Univ Stuttgart, Inst Modelling Hydraul & Environm Syst, D-70569 Stuttgart, Germany.
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- Yotov, Ivan (författare)
- Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA.
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(creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2022
- 2022
- Engelska.
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 60:3, s. 1193-1225
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We investigate a mortar technique for mixed finite element approximations of a class of domain decomposition saddle point problems on nonmatching grids in which the variable associated with the essential boundary condition, referred to as flux, is chosen as the coupling variable. It plays the role of a Lagrange multiplier to impose weakly continuity of the variable associated with the natural boundary condition. The flux-mortar variable is incorporated with the use of a discrete extension operator. We present well-posedness and error analysis in an abstract setting under a set of suitable assumptions, followed by a nonoverlapping domain decomposition algorithm that reduces the global problem to a positive definite interface problem. The abstract theory is illustrated for Darcy flow, where the normal flux is the mortar variable used to impose continuity of pressure, and for Stokes flow, where the velocity vector is the mortar variable used to impose continuity of normal stress. In both examples, suitable discrete extension operators are developed and the assumptions from the abstract theory are verified. Numerical studies illustrating the theoretical results are presented for Darcy flow.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- mixed finite element
- domain decomposition
- nonmatching grids
- a priori error analysis
- flux-mortar method
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- art (ämneskategori)
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