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## Program

Mo 8.10. | Tu
9.10. | |
---|---|---|

9.45 | Welcome | |

10.00 | Peter Deuflhard
(Berlin)Tales from the Dawn of
Harrychical Finite Elements | Jinchao Xu
(University Park)Preconditioning
Techniques Based on Auxiliary Discretizations
(Abstract) |

10.45 | Coffee | Coffee |

11.30 | Peter Leinen
(Mannheim)Infrastructures for
Research Communities | Gerhard
Huisken (Potsdam)Analytical and Geometrical
Properties of Inverse Mean Curvature Flow
(Abstract) |

12.15 | Lunch | Lunch |

14.00 | Christian Lubich
(Tübingen)Variational Approximations in
Quantum Dynamics | Wolfgang Hackbusch
(Leipzig)Maximum Norm Estimates for SVD Truncated Tensors
(Abstract) |

14.45 | tba | Folkmar
Bornemann (München)Striving for Simplicity: A
Numerical Analyst Poaching in Mathematical Physics
(Abstract) |

16.00 | Festive
reception in the mathematical libraryRoom MA 163 (math building) | 15.30 Coffee |

16.15 | Randy Bank
(San Diego)On the H
(Abstract)^{1}-stability of the
L_{2}-Projection onto Finite Element Spaces | |

19.00 | Conference
dinner atNeugrüns Köche [1] Schönhauser Allee 135 a, 10437 BerlinBus transfer from TU Berlin at
18.30 |

**Randy Bank, Harry
Yserentant **

*On the H*

^{1}-stability of the L_{2}-Projection onto Finite Element SpacesWe study the stability in the $H^1$-seminorm of the $L_2$-projection onto finite element spaces, in the case of nonuniform but shape regular meshes in two and three dimensions. We prove stability for piecewise linear elements in 2d and 3d, and piecewise quadratic elements in 2d for meshes where neighboring elements differ by at most a factor of two in diameter. For less strongly graded meshes, our proof shows stability for a much broader class of finite element spaces.

**Folkmar Bornemann **

*Striving for Simplicity: A Numerical Analyst Poaching in Mathematical Physics*

The numerical evaluation of operator determinants, originally born out of an attempt to validate some PDE calculations, has become a popular tool in areas of Mathematical and Theoretical Physics dealing with integrable systems; e..g., it was recently used by Nishigaki to calculate the `pion decay constant` of certain QCD-like theories. We review some of this development, tell an amusing story about the numerical evaluation of higher-order derivatives and its relation to a problem in graph theory, and show how a numerical analyst can be trapped into an attempt to simplify some purely mathematical theory.

**Wolfgang Hackbusch**

*Maximum Norm Estimates for SVD Truncated Tensors*

The standard HOSVD truncation of tensors yields a controlled error with respect to the corresponding Hilbert norm, usually L2-norm. If the tensor represents a multivariate function, the aim may be to evaluate the function at certain points. Therefore, we need maximum error estimates instead. Usually, the maximum norm cannot be estimated by the L2-norm. We show that, nevertheless, this is possible for the HOSVD truncated tensors.

**Gerhard Huisken**

*Analytical and Geometrical Properties of Inverse Mean Curvature Flow*

When a hypersurface moves in normal direction with speed equal to the inverse of its (positive) mean curvature, the area of the surface grows exponentially everywhere while this nonlinear parabolic expansion is smoothing out the surface. The lecture gives an overview of properties of this flow including recent applications in Geometry and General Relativity.

**Jinchao Xu**

*Preconditioning Techniques Based on Auxiliary Discretizations*

In this talk, I will report several recent results on using an auxiliary discretization as a main ingredient in designing preconditioner for discretized PDEs. One such result is that the discretized system for a class of 4th order problems can be preconditioned by using a mixed finite element discretization that is not always convergent as a discretization scheme alone. The general framework of Fast Auxiliary Space Preconditioning (FASP) methods will be used in the design and analysis of this type of methods.