401-3651-00L  Numerical Methods for Elliptic and Parabolic Partial Differential Equations (University of Zurich)

SemesterHerbstsemester 2017
DozierendeS. Sauter
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch
KommentarCourse 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.

Der Kurs muss direkt an der UZH belegt werden.
UZH Modulkürzel: MAT802

Beachten Sie die Einschreibungstermine an der UZH: Link



Lehrveranstaltungen

NummerTitelUmfangDozierende
401-3651-00 VNumerical Methods for Elliptic and Parabolic Partial Differential Equations (Universitiy of Zurich)
**Course at University of Zurich**
4 Std.
Mi08:00-09:45UNI ZH .
Do08:00-09:45UNI ZH .
S. Sauter
401-3651-00 UNumerical Methods for Elliptic and Parabolic Partial Differential Equations (Universitiy of Zurich)
**Course at University of Zurich**
1 Std.n. V.S. Sauter
401-3651-00 PNumerical Methods for Elliptic and Parabolic Partial Differential Equations (Universitiy of Zurich)
**Course at University of Zurich**
1 Std.n. V.S. Sauter

Katalogdaten

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

Leistungskontrolle

Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte10 KP
PrüfendeS. Sauter
Formbenotete Semesterleistung
PrüfungsspracheEnglisch
RepetitionRepetition nur nach erneuter Belegung der Lerneinheit möglich.
Zusatzinformation zum PrüfungsmodusRegistration modalities, date and venue of this performance assessment are specified solely by the UZH.

Lernmaterialien

Keine öffentlichen Lernmaterialien verfügbar.
Es werden nur die öffentlichen Lernmaterialien aufgeführt.

Gruppen

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Einschränkungen

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Doktorat Departement MathematikGraduate School / GraduiertenkollegWInformation
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Mathematik MasterKernfächer aus Bereichen der angewandten Mathematik ...WInformation