A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow
DOI10.1016/j.cma.2018.12.040zbMath1440.76073arXiv1807.07790OpenAlexW2883275932WikidataQ114196942 ScholiaQ114196942MaRDI QIDQ1987830
Gianluigi Rozza, Guglielmo Scovazzi, Giovanni Stabile, Léo Nouveau, Efthimios N. Karatzas
Publication date: 16 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.07790
Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Boundary element methods applied to problems in fluid mechanics (76M15) Finite element methods applied to problems in fluid mechanics (76M10) Boundary element methods for boundary value problems involving PDEs (65N38)
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Cites Work
- A numerical investigation of velocity-pressure reduced order models for incompressible flows
- Nonlinear model reduction for the Navier-Stokes equations using residual DEIM method
- Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants
- The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
- On the stability and extension of reduced-order Galerkin models in incompressible flows. A numerical study of vortex shedding
- Proper general decomposition (PGD) for the resolution of Navier-Stokes equations
- Parametric free-form shape design with PDE models and reduced basis method
- The shifted boundary method for hyperbolic systems: embedded domain computations of linear waves and shallow water flows
- Reduction of nonlinear embedded boundary models for problems with evolving interfaces
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- Enablers for robust POD models
- On the stability of the reduced basis method for Stokes equations in parametrized domains
- A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
- A new finite element formulation for computational fluid dynamics. VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
- A discourse on the stability conditions for mixed finite element formulations
- Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds.
- Stability properties of POD-Galerkin approximations for the compressible Navier-Stokes equations
- Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations
- POD-Galerkin reduced order methods for CFD using finite volume discretisation: vortex shedding around a circular cylinder
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Stability and accuracy of periodic flow solutions obtained by a POD-penalty method
- The shifted boundary method for embedded domain computations. I: Poisson and Stokes problems
- The shifted boundary method for embedded domain computations. II: Linear advection-diffusion and incompressible Navier-Stokes equations
- Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13--16, 2015
- A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection
- Flow patterns around heart valves: A numerical method
- Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations
- On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment
- IMMERSED BOUNDARY METHODS
- Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
- Numerical solution of parametrized Navier–Stokes equations by reduced basis methods
- The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows
- Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
- Certified Reduced Basis Methods for Parametrized Saddle Point Problems
- Computational Fluid–Structure Interaction
- Mixed Finite Element Methods and Applications
- Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation
- A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations
- Reduced Basis Methods for Partial Differential Equations
- An arbitrary Lagrangian-Eulerian computing method for all flow speeds
- Reduced basis methods for Stokes equations in domains with non-affine parameter dependence