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

SemesterAutumn Semester 2018
LecturersS. Sauter
Periodicityyearly recurring course
Language of instructionEnglish
CommentCourse 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.

No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH.
UZH Module Code: MAT802

Mind the enrolment deadlines at UZH:
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Courses

NumberTitleHoursLecturers
401-3651-00 VNumerical Methods for Elliptic and Parabolic Partial Differential Equations (Universitiy of Zurich)
**Course at University of Zurich**
4 hrs
Wed08:00-09:45UNI ZH .
Thu08:00-09:45UNI ZH .
S. Sauter
401-3651-00 UNumerical Methods for Elliptic and Parabolic Partial Differential Equations (Universitiy of Zurich)
**Course at University of Zurich**
Wed 10-12 or Thu 10-12
2 hrs
Wed10:15-12:00UNI ZH .
Thu10:15-12:00UNI ZH .
S. Sauter

Catalogue data

AbstractThis 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.
ObjectiveParticipants 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
ContentA 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 notesCourse slides will be made available to the audience.
LiteratureS. 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).
Prerequisites / NoticePractical exercises based on MATLAB

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits9 credits
ExaminersS. Sauter
Typegraded semester performance
Language of examinationEnglish
RepetitionRepetition only possible after re-enrolling for the course unit.
Additional information on mode of examinationRegistration modalities, date and venue of this performance assessment are specified solely by the UZH.

Learning materials

No public learning materials available.
Only public learning materials are listed.

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics BachelorCore Courses: Applied Mathematics and Further Appl.-Oriented FieldsWInformation
Mathematics MasterCore Courses: Applied Mathematics and Further Appl.-Oriented FieldsWInformation