Reduced Basis Method for Optimal Control of Unsteady Viscous Flows

By Kazufumi Ito, S. S. Ravindran. 2001

82 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/053ca2ec8221656b58b6c32559eeed7d6b077400

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Gianluigi Rozza
2. Andrea Manzoni
3. Alfio Maria Quarteroni
4. Jan S. Hesthaven
5. Anthony T. Patera
6. Martin A. Grepl
7. Ngoc Cuong Nguyen
8. David J. Knezevic

In Statistical and Nonlinear Physics

1. Gianluigi Rozza
2. Andrea Manzoni
3. Alfio Maria Quarteroni
4. Anthony T. Patera
5. Martin A. Grepl
6. Jan S. Hesthaven
7. Ngoc Cuong Nguyen
8. David J. Knezevic

Citations in the corpus

• Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “The next decade(s) saw further expansion into different applications and classes of equations, such as fluid dynamics and the Navier-Stokes equations [57, 65, 66, 67, 68, 112].”
• Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation (2009, background): “Although there are many examples of reduced order models for the unsteady incompressible Navier–Stokes equations [5,7,9,13,14,17–21], none is endowed with rigorous a posteriori error bounds.”
• Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, unknown): “[284] K.”
• A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, background): “, of the variety described above) are often employed: applications range from fluid flow [16–18, 36] to hyperthermia treatment [24, 25] to thermal processing of semiconductors [30] and canned foods [4].”
• REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS (2011, background): “However, none of the earlier examples of reduced order models for the unsteady incompressible NavierStokes and Boussinesq equations [7,9,12,22,23,30–33] is endowed with practicable and rigorous error bounds.”
• Certified reduced basis approximation for parametrized partial differential equations and applications (2011, background): “The next decade saw further expansion into different applications and classes of equations, such as fluid dynamics and, more specifically, the incompressible Navier-Stokes equations, [13, 14, 15, 16].”