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Title:
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Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem
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Author:
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Badia, Santiago; Martín Huertas, Alberto Francisco; Verdugo Rojano, Francesc
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Other authors:
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Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. ANiComp - Anàlisi numèrica i computació científica |
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Abstract:
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Abstract:
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In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that these kinds of methods lead to arbitrarily ill-conditioned systems and poorly approximated fluxes on unfitted interfaces/boundaries. In order to solve these issues, we consider the recently proposed aggregated finite element method, originally motivated for coercive problems. However, the well-posedness of the Stokes problem is far more subtle and relies on a discrete inf-sup condition. We consider mixed finite element methods that satisfy the discrete version of the inf-sup condition for body-fitted meshes and analyze how the discrete inf-sup is affected when considering the unfitted case. We propose different aggregated mixed finite element spaces combined with simple stabilization terms, which can include pressure jumps and/or cell residuals, to fix the potential deficiencies of the aggregated inf-sup. We carry out a complete numerical analysis, which includes stability, optimal a priori error estimates, and condition number bounds that are not affected by the small cut cell problem. For the sake of conciseness, we have restricted the analysis to hexahedral meshes and discontinuous pressure spaces. A thorough numerical experimentation bears out the numerical analysis. The aggregated mixed finite element method is ultimately applied to two problems with nontrivial geometries. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
-Navier-Stokes equations--Numerical solutions
-embedded boundary
-unfitted finite elements
-Stokes
-inf-sup
-conditioning
-Equacions de Navier-Stokes -- Mètodes numèrics |
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Rights:
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Document type:
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Article - Published version
Article |
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