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401-3663-00L 12 Credits BSC , DS , MSC D-HEST , D-PHYS , D-MAVT , D-ITET , D-INFK , D-MATH
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Numerical Solution of Differential Equations

Numerik der Differentialgleichungen

Lecturers: Dr. Alexey Chernov
Examiners: Prof. Dr. Christoph Schwab
VVZ CR n/a

Last Updated: 2026-02-05 15:14:53

Abstract

Methods for the numerical solution of partial differential equations of elliptic, parabolic and hyperbolictype. Finite Element, Finite Difference and Finite Volume Methods. A-priori and a-posteriorierror estimation. MATLAB implementation in one and two spatial dimensions.

Objective

Overview of the most important methods for numerical solution of partial differential equations, in particular of linear elliptic, parabolic and hyperbolic partial differential equations. Overview of the theory plus implementation of the methods.

Content

Elliptic problems. Diffusion. Finite Element Methods, Finite Difference Methods: analysis and implementation. Direct and iterative solution of linear systems of equations. A-priori and a-posteriori error estimation. Adaptive Mesh Refinement Algorithms in 1-d and in 2-d. Indefinite Problems of Helmholtz type. Problems with constraints. Stokes Problem. Inf-sup Condition and divergence stable Finite Elements. Eigenvalue problems and their FE discretization. Linear parabolic problems. Explicit and implicit timestepping schemes. Finite Difference Methods for linear and nonlinear hyperbolic problems in one space dimension.

Resources

Lecture Notes

Skript is provided.

Literature

D. Braess, Finite Elements, Cambridge Univ. Press

General Information

Language
English
Levels
BSC , DS , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
10 DIN A4 Blätter beidseitig handschriftlich beschrieben, Taschenrechner.

Course Components

Type Title Time & Place Hours
lecture Numerik der Differentialgleichungen (Numerical Solution of Differential Equations)
  • Wed 10:15-12:00 (HG D 7.2)
  • Thu 10:15-12:00 (HG D 5.2)
4 h weekly
exercise Numerik der Differentialgleichungen (Numerical Solution of Differential Equations)
  • Mon 08:15-10:00 (HG D 1.2)
2 h weekly

Offered In