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Diese Vorlesung betrachtet lineare Sattelpunktprobleme und gemischte
Finite-Elemente. Die folgenden Themen werden behandelt:
* Herleitung der Navier-Stokes-Gleichungen, der Grundgleichungen der Strömungsmechanik
* Existenz und Eindeutigkeit der Lösung eines linearen Sattelpunktproblems
* geeignete Finite-Elemente-Methoden für inkompressible Strömungsprobleme
* Anwendung der Theorie auf die Finite-Element Analysis der Stokes-Gleichungen
* stabilisierte Finite-Elemente für die Stokes-Gleichungen

Voraussetzungen: Basiswissen über Numerik partieller Differentialgleichungen, z.B. durch Numerik III

Literatur: V. John, "Finite Element Methods for Incompressible Flow Problems", Springer Series in Computational Mathematics, Vol. 51, Springer, 2016

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This course considers linear saddle point problems and mixed finite element
methods. The following topics will be included:
* derivation of the Navier-Stokes equations, the fundamental equations of fluid dynamics
* existence and uniqueness of the solution of linear saddle point problems
* application of the theory to the finite element analysis of the Stokes equations
* stabilized finite element methods for the Stokes equations

Prerequisites: basic knowledge on numerical methods for partial differential
equations, e.g., from Numerical Mathematics III

Literature: V. John, "Finite Element Methods for Incompressible Flow Problems", Springer Series in Computational Mathematics, Vol. 51, Springer, 2016

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