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401-3651-00L  Numerical Methods for Elliptic and Parabolic Partial Differential Equations

SemesterAutumn Semester 2016
LecturersC. Schwab
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.



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.
Literaturen.a.
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 credits10 credits
ExaminersC. Schwab
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Admission requirementPassed examination blocks I and II from the ETH bachelor's degree programme in mathematics or equivalent.
Mode of examinationoral 30 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkLink to the lecture webpage
Only public learning materials are listed.

Courses

NumberTitleHoursLecturers
401-3651-00 VNumerical Methods for Elliptic and Parabolic Partial Differential Equations4 hrs
Tue15-17HG E 33.1 »
Thu13-15HG D 7.2 »
C. Schwab
401-3651-00 UNumerical Methods for Elliptic and Parabolic Partial Differential Equations1 hrs
Mon17-18HG E 21 »
C. Schwab

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