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401-3651-00L 9 Credits BSC , MSC D-MATH
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Numerical Methods for Elliptic and Parabolic Partial Differential Equations (University of Zurich)

No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH as an incoming student. UZH Module Code: MAT802 Mind the enrolment deadlines at UZH: 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.
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Last Updated: 2026-06-01 11:31:23

Abstract

This course gives a comprehensive introduction into the numerical treatment of elliptic boundary value problems and parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods.Practical exercises include MATLAB and python implementations of finite difference methods, finite element methods and time integration schemes.

Objective

Participants 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

Content

The course will address the mathematical analysis of numerical solution methods for elliptic and parabolic partial differential equations. Functional analytic tools (Sobolev spaces) and the basic analysis of partial differential equations is discussed in the course. Particular attention will be placed on developing mathematical foundations for a-priori convergence rate analysis. The basic ideas behind a-posteriori error analysis and adaptivity are covered. Implementations for model problems in MATLAB and python will illustrate the theory.

Resources

Literature

The bulk of the lecture is based on the script. Some excerpts from the first chapter of the following reference may be used as well. Bartels, Sören: Numerical approximation of partial differential equations. Texts in Applied Mathematics, 64. Springer, New York, 2016 Additional Literature: Brenner, Susanne C.; Scott, L. Ridgway The mathematical theory of finite element methods. Third edition. Texts in Applied Mathematics, 15. Springer, New York, 2008. xviii+397 pp. 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 D. Braess: Finite Elements, THIRD Ed., Cambridge Univ. Press, (2007). (Also available in German.) Brezis, Haim Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. xiv+599 pp. 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).

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
graded semester performance
Registration modalities, date and venue of this performance assessment are specified solely by the UZH.

Course Components

Type Title Time & Place Hours
lecture Numerical Methods for Elliptic and Parabolic Partial Differential Equations (University of Zurich) No time listed 4 h weekly
exercise Numerical Methods for Elliptic and Parabolic Partial Differential Equations (University of Zurich) No time listed 2 h weekly

Offered In