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401-0674-AAL 10 Credits MSC D-MATH
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Numerical Methods for Partial Differential Equations

Lecturers & Examiners: Prof. Dr. Ralf Hiptmair
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: 2026-02-05 16:37:17

Abstract

Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations,among them (convection)-diffusion and heat equations, 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

See the contents of 401-0674-00 Numerical Methods for Partial Differential Equations

Resources

Lecture Notes

The lecture will be taught in flipped classroom format:- Video tutorials for all thematic units will be published online.- Tablet notes accompanying the videos will be made available to the audience as PDF.- A comprehensive PDF handout will cover all aspects of the lecture.

Literature

See the information given for 401-0674-00 Numerical Methods for Partial Differential Equations

General Information

Language
English
Levels
MSC
Frequency
Semesterly recurring

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.
Three-hour (180 minute) computer based examination involving coding problems beside theoretical questions. Some of the lecture materials and other documents will be made available as PDF or HTML during the examination. The total exam time of 225 minute also include 30-minute reading time in the beginning of the exam.A 30-minute mid-term exam and a 30-minute end term exam (non-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.

Course Components

Type Title Time & Place Hours
revision course / private study Numerical Methods for Partial Differential Equations
Self-study course. No presence required. Attendance of parallel flipped-classroom course strongly recommended. IMPORTANT: Please also register for the actual course unit 401-0674-00 G Numerical Methods for Partial Differential Equations in order to be included in communication. This "course" is listed for formal reasons only.
No time listed 300 h semesterly

Offered In