Christoph Schwab: Katalogdaten im Herbstsemester 2016

NameHerr Prof. Dr. Christoph Schwab
LehrgebietMathematik
Adresse
Seminar für Angewandte Mathematik
ETH Zürich, HG G 57.1
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 35 95
Fax+41 44 632 10 85
E-Mailchristoph.schwab@sam.math.ethz.ch
URLhttp://www.sam.math.ethz.ch/~schwab
DepartementMathematik
BeziehungOrdentlicher Professor

NummerTitelECTSUmfangDozierende
401-3640-66LMonte Carlo and Quasi-Monte Carlo Methods: Mathematical and Numerical Analysis Belegung eingeschränkt - Details anzeigen
Maximale Teilnehmerzahl: 6
4 KP2SC. Schwab
KurzbeschreibungIntroduction and current research topics in the theory and implementation of Monte Carlo and quasi-Monte Carlo methods and applications.
Lernziel
Voraussetzungen / BesonderesPrerequisites:
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.
401-3651-00LNumerical Methods for Elliptic and Parabolic Partial Differential Equations Information
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 KP4V + 1UC. Schwab
KurzbeschreibungThis 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.
LernzielParticipants 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
InhaltA 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
SkriptCourse slides will be made available to the audience.
LiteraturS. C. Brenner and L. Ridgway Scott: The mathematical theory of Finite Element Methods. New York, Berlin [etc]: Springer-Verl, cop.1994.

A. Ern and J.L. Guermond: Theory and Practice of Finite Element Methods,
Springer Applied Mathematical Sciences Vol. 159, Springer,
1st Ed. 2004, 2nd Ed. 2015.

R. Verfürth: A Posteriori Error Estimation Techniques for Finite Element Methods, Oxford University Press, 2013

Additional Literature:
D. Braess: Finite Elements, THIRD Ed., Cambridge Univ. Press, (2007).
(Also available in German.)

D. A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, vol. 69 SMAI Mathématiques et Applications,
Springer, 2012 [DOI: 10.1007/978-3-642-22980-0]

V. Thomee: Galerkin Finite Element Methods for Parabolic Problems,
SECOND Ed., Springer Verlag (2006).
Voraussetzungen / BesonderesPractical exercises based on MATLAB
401-5650-00LZurich Colloquium in Applied and Computational Mathematics Information 0 KP2KR. Abgrall, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab
KurzbeschreibungResearch colloquium
Lernziel