Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport



Methodology: Seminar Presentations

We include here selected recent presentations of our group relevant to reduced basis approximation and a posteriori error estimation. Back to new list »

1. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, College de France, 8 June 2007; Reliable Real-Time Solution of Parametrized PDEs, ENPC/CERMICS, Paris, 12 June 2007. pdf slideshow (presentations combined into one set of slides)

2. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, AFOSR Joint Program Review, Long Beach, CA, 7 August 2007.pdf slideshow (presentation) pdf digest (presentation in digest form for printing)

3. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, AFOSR Joint Program Review, Washington, DC, 14 August 2008.pdf slideshow (presentation)
ERRATA We have discovered that the exponential stability factors reported in the talk for Navier-Stokes are in error — and in the wrong direction: the error bounds reported are thus not rigorous and in particular too optimistic. The theory is correct; however, it is now clear that the theory as presented is practically restricted to much smaller times or lower Reynolds number than claimed in the paper. We will report elsewhere on improvements to the theory and associated (new) computational results.
Correct Navier-Stokes/Boussinesq results may be found in Paper 34.

4. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (for Uncertainty Quantification), OPUS Workshop, Paris/Clamart EDF, 8 October 2008.pdf slideshow (presentation)
ERRATA We have discovered that the exponential stability factors reported in the talk for Navier-Stokes are in error — and in the wrong direction: the error bounds reported are thus not rigorous and in particular too optimistic. The theory is correct; however, it is now clear that the theory as presented is practically restricted to much smaller times or lower Reynolds number than claimed in the paper. We will report elsewhere on improvements to the theory and associated (new) computational results. There is also a small error in the L2 error bound, Slide 129, and associated numerical results. A corrected version of the L2 error bound may be found in Paper 31.
Correct Navier-Stokes/Boussinesq results may be found in Paper 34.

5. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations. Special Guest: Navier-Stokes — Cameo Appearance: Wave Equation , Brown University, 5 December 2008.pdf slideshow (presentation)
ERRATA We have discovered that the exponential stability factors reported in the talk for the Navier-Stokes and Boussinesq equations are in error — and in the wrong direction: the error bounds reported are thus not rigorous and in particular too optimistic. The theory is correct; however, it is now clear that the theory as presented is practically restricted to much smaller times or lower Reynolds/Grashof number than claimed in the paper. We will report elsewhere on improvements to the theory and associated (new) computational results. There is also a small error in the L2 error bound, Slide 115, and associated numerical results. A corrected version of the L2 error bound may be found in Paper 31.
Correct Navier-Stokes/Boussinesq results may be found in Paper 34.

6. AT Patera, Certified Reduced Basis Methods: Application to Heat Transfer and Incompressible Fluid Flow, Fifth MIT Conference on Computational Fluid and Solid Mechanics, 17 June 2009.pdf slideshow (presentation)
ERRATA We have discovered that the exponential stability factors reported in the talk for the Boussinesq equations are in error — and in the wrong direction: the error bounds reported are thus not rigorous and in particular too optimistic. The theory is correct; however, it is now clear that the theory as presented is practically restricted to much smaller times or lower Grashof number than claimed in the paper. We will report elsewhere on improvements to the theory and associated (new) computational results. There is also a small error in the L2 error bound, Slide 53, and associated numerical results. A corrected version of the L2 error bound may be found in Paper 31.
Correct Navier-Stokes/Boussinesq results may be found in Paper 34.

7. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, AFOSR Computational Math Program Review, Arlington, VA, 29–31 July 2009.pdf slideshow (presentation)
ERRATA We have discovered that the exponential stability factors reported in the talk for the Boussinesq equations are in error — and in the wrong direction: the error bounds reported are thus not rigorous and in particular too optimistic. The theory is correct; however, it is now clear that the theory as presented is practically restricted to much smaller times or lower Grashof number than claimed in the paper. We will report elsewhere on improvements to the theory and associated (new) computational results. Note the part of the talk on hyperbolic equations is free of (known) errors.
Correct Navier-Stokes/Boussinesq results may be found in Paper 34.

8. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for the 2nd-Order Wave Equation, ICOSAHOM ’09, Trondheim, Norway, 23 June 2009. pdf slideshow (presentation)

9. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, MoRePaS 09, Münster, Germany, 16–18 September 2009. pdf slideshow (presentation)

10. AT Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, Rocca Day, Politecnico di Milano, 28 September 2009; and MOX, Dipartimento di Matematica, Politecnico di Milano, 29 September 2009. pdf slideshow (presentations combined into one set of slides)

11. AT Patera, Model Order Reduction; Rigorous Error Control, OSD/AFOSR MURI Kick-Off Meeting, Brown University, Providence, RI, 30 October 2009. pdf slideshow (presentation)

12. AT Patera, Certified Reduced Basis Methods; Application to Continuum Mechanics and Transport, MechSE Seminar Series, University of Illinois at Urbana-Champaign, Urbana, IL, 1 December 2009. pdf slideshow (presentation)

13. AT Patera, Certified Reduced Basis Methods; Application to Continuum Mechanics and Transport, Symposium on High Accuracy Flow Simulations in Honor of Professor Michel Deville, Ecole Polytechnique Fédérale de Lausanne, Switzerland, 15–16 February 2010. pdf slideshow (presentation)

 

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