Numerics of Partial Differential Equations (NumPDE)10 ECTS
(englische Bezeichnung: Numerics of Partial Differential Equations)
(Prüfungsordnungsmodul: Numerics of Partial Differential Equations)

Lectures:

• • Numerics of Partial Differential Equations I
    (Vorlesung, 4 SWS, Günther Grün, Tue, 10:00 - 12:00, H12; Fri, 8:00 - 10:00, Übung 2 / 01.251-128; single appointment on 29.10.2019, 10:00 - 12:00, KS I)

Empfohlene Voraussetzungen:

Recommended: basic knowledge in numerics, discretization, and optimization

Inhalt:

• Classical theory of linear elliptic boundary value problems (outline) Finite difference method (FDM) for Poisson’s equation in two dimensions (including stability via inverse monotonicity)

Finite element method (FEM) for Poisson’s equation in two dimensions (stability and convergence, example: linear finite elements, implementation)

• Variational theory of linear elliptic boundary value problems (outline)

FEM for linear elliptic boundary value problems (2nd order) (types of elements, affin equivalent triangulations, order of convergence, maximum principle)

• Iterative methods for large sparse linear systems of equations (condition number of finite element matrices, linear stationary methods (recall), cg method (recall), preconditioning, Krylov subspace methods

Lernziele und Kompetenzen:

Students

• apply algorithmic approaches for models with partial differential equations and explain and evaluate them,

• are capable to judge on a numerical method’s properties regarding stability and efficiency,

• implement (with own or given software) numerical methods and critically evaluate the results,

• explain and apply a broad spectrum of problems and methods with a focus on conforming finite element methods for linear elliptic problems,

• collect and evaluate relevant information and realize relationships.

Literatur:

• P. Knabner & L. Angermann: Numerical Methods for Elliptic and Parabolic Differential Equations, Springer 2003

• S. Larssen & V. Thomee: Partial Differential Equations with Numerical Methods. Springer 2005

• D. Braess: Finite Elements. Cambridge University Press 2010

• lecture scripts on the homepage of the domain Modeling, Simulation, and Optimization of the department Mathematics, frequently updated

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Computational and Applied Mathematics (Master of Science)
   (Po-Vers. 2019w | NatFak | Computational and Applied Mathematics (Master of Science) | Gesamtkonto | Specialisation: Modeling and applied analysis (MApA) and numerical analysis and simulation (NASi) | Numerics of Partial Differential Equations)
2. Computational and Applied Mathematics (Master of Science)
   (Po-Vers. 2019w | NatFak | Computational and Applied Mathematics (Master of Science) | Gesamtkonto | Specialisation: Numerical analysis and simulation (NASi) and optimization (Opti) | Numerics of Partial Differential Equations)
3. Computational and Applied Mathematics (Master of Science)
   (Po-Vers. 2019w | NatFak | Computational and Applied Mathematics (Master of Science) | Gesamtkonto | Non-Specialisation modules | Numerics of Partial Differential Equations)

Studien-/Prüfungsleistungen:

Numerics of Partial Differential Equations (Prüfungsnummer: 59931)

Prüfungsleistung, Klausur, Dauer (in Minuten): 90, benotet, 10 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Erstablegung: WS 2019/2020, 1. Wdh.: SS 2020

1. Prüfer:

Günther Grün