## Christoph Schwab: Catalogue data in Autumn Semester 2016 |

Name | Prof. Dr. Christoph Schwab |

Field | Mathematik |

Address | Seminar für Angewandte Mathematik ETH Zürich, HG G 57.1 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 35 95 |

Fax | +41 44 632 10 85 |

christoph.schwab@sam.math.ethz.ch | |

URL | http://www.sam.math.ethz.ch/~schwab |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-3640-66L | Monte Carlo and Quasi-Monte Carlo Methods: Mathematical and Numerical Analysis Number of participants limited to 6. | 4 credits | 2S | C. Schwab | |

Abstract | Introduction and current research topics in the theory and implementation of Monte Carlo and quasi-Monte Carlo methods and applications. | ||||

Learning objective | |||||

Prerequisites / Notice | Prerequisites: Completed courses Numerical Analysis of Elliptic/ Parabolic PDEs, or Numerical Analysis of Hyperbolic PDEs, or Numerical Analysis of Stochastic ODEs, and FAI, Probability Theory I. | ||||

401-3651-00L | Numerical Methods for Elliptic and Parabolic Partial Differential Equations Course audience at ETH: 3rd year ETH BSc Mathematics and MSc Mathematics and MSc Applied Mathematics students. Other ETH-students are advised to attend the course "Numerical Methods for Partial Differential Equations" (401-0674-00L) in the CSE curriculum during the spring semester. | 10 credits | 4V + 1U | C. Schwab | |

Abstract | This course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems, related eigenvalue problems and linear, parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises include MATLAB implementations of finite element methods. | ||||

Learning objective | Participants of the course should become familiar with * concepts underlying the discretization of elliptic and parabolic boundary value problems * analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems * methods for the efficient solution of discrete boundary value problems * implementational aspects of the finite element method | ||||

Content | A selection of the following topics will be covered: * Elliptic boundary value problems * Galerkin discretization of linear variational problems * The primal finite element method * Mixed finite element methods * Discontinuous Galerkin Methods * Boundary element methods * Spectral methods * Adaptive finite element schemes * Singularly perturbed problems * Sparse grids * Galerkin discretization of elliptic eigenproblems * Non-linear elliptic boundary value problems * Discretization of parabolic initial boundary value problems | ||||

Lecture notes | Course slides will be made available to the audience. | ||||

Literature | n.a. | ||||

Prerequisites / Notice | Practical exercises based on MATLAB | ||||

401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics | 0 credits | 2K | R. Abgrall, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab | |

Abstract | Research colloquium | ||||

Learning objective |