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401-0674-AAL 10 Credits MSC D-MATH

Numerical Methods for Partial Differential Equations

Does not take place this semester. Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
VVZ CR 2.4

Last Updated: 2026-06-01 11:31:29

Abstract

Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations: convection-diffusion, heat equation, wave equation, conservation laws. Implementation in C++ based on a finite element library.

Objective

Main skills to be acquired in this course: * Ability to implement fundamental numerical methods for the solution of partial differential equations efficiently. * Ability to modify and adapt numerical algorithms guided by awareness of their mathematical foundations. * Ability to select and assess numerical methods in light of the predictions of theory * Ability to identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm. * Ability to understand research publications on theoretical and practical aspects of numerical methods for partial differential equations. * Skills in the efficient implementation of finite element methods on unstructured meshes. This course is neither a course on the mathematical foundations and numerical analysis of methods nor an course that merely teaches recipes and how to apply software packages.

Content

Second-Order Scalar Elliptic Boundary Value Problems Finite Element Methods (FEM) FEM: Convergence and Accuracy Beyond FEM: Alternative Discretizations Non-Linear Elliptic Boundary Value Problems Second-Order Linear Evolution Problems Finite-Element Exterior Calculus (FEEC) Finite Elements for the Stokes Equation

Resources

Lecture Notes

The lecture will be taught in flipped classroom format:- Video tutorials for all thematic units will be published online.- Solution of homework problems will partly be covered by video tutorials.- Lecture documents and tablet notes accompanying the videos will be made available to the audience as PDF.

Literature

Chapters of the following books provide supplementary reading (detailed references in course material): * D. Braess: Finite Elemente, Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Springer 2007 (available online). * S. Brenner and R. Scott. Mathematical theory of finite element methods, Springer 2008 (available online). * A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer, New York, 2004. * Ch. Großmann and H.-G. Roos: Numerical Treatment of Partial Differential Equations, Springer 2007. * W. Hackbusch. Elliptic Differential Equations. Theory and Numerical Treatment, volume 18 of Springer Series in Computational Mathematics. Springer, Berlin, 1992. * P. Knabner and L. Angermann. Numerical Methods for Elliptic and Parabolic Partial Differential Equations, volume 44 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * S. Larsson and V. Thomée. Partial Differential Equations with Numerical Methods, volume 45 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * R. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK, 2002. However, study of supplementary literature is not important for for following the course.

General Information

Language
English
Levels
MSC

Examination

Type
session examination
Mode
written 225 minutes
Aids
No aids allowed. Some documentations and documents will be made available on the exam computers.
Digital
The exam takes place on devices provided by ETH Zurich.
Computer based examination involving coding problems beside theoretical questions. Some of the lecture materials will be made available as PDF during the examination. The total exam time of 225 minutes includes 30 minutes of advance reading time.Same exam as for the course unit 401-0674-00L, which is taught during the spring semester and where a 30-minutes mid-term exam and a 30-minutes end-term exam (both not mandatory) will be held during the teaching period on dates specified in the beginning of the semester. The grades of these interim examinations will be taken into account through a bonus of up to 30% for the final grade. The bonus can also be acquired by students who must take the performance assessment for the course unit 406-0674-AAL if they take part in the exams during the semester. The dates for the term exams will be communicated in the beginning of the course 406-0674-00L.

Course Components

Type Title Time & Place Hours
revision course / private study Numerical Methods for Partial Differential Equations
Does not take place this semester. Self-study course based on video tutorial and lecture notes. No presence required. BEMERKUNG: diese spezielle -AA LV für eine Auflagen-LE löschen, falls möglich. Findet nicht mehr statt. Als Auflage wird nur noch die echte LE angeboten, welche jeweils im FS stattfindet.
No time listed 300 h semesterly

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