Lehrinhalte
Modelling: Reynolds transport theorem; conservation of mass and momentum; Navier-Stokes and Euler equations; boundary conditions; siomplified models;
Analysis: weak formulation; existence and uniqueness results for Stokes and Navier-Stokes;
Numerics: The finite element method for coercive and non-coercive problems; convergence analysis; convection-diffusion problems; stable discretization for the Stokes problem; numerical tretament of the Navier-Stokes equations;
Literature
D. Braess: Finite Elemente, Springer.
D. C. Brenner, L. R. Scott: The mathematical theory of finite element methods, Springer.
V. Girault, P.-A. Raviart: Finite Element Approximation of the Navier-Stokes Equations, Springer.
C. Johnson: Numerical solution of partial differential equations by the finite element method, Dover.
R. Temam, Navier-Stokes Equations, North-Holland Publishing.
Voraussetzungen
recommended: required: basic knowledge of partial differential equations and numerical methods
useful courses: Functional Analysis, Partial Differential Equations, Numerical Analysis of Elliptic/Parabolic Differential Equations
Modelling: Reynolds transport theorem; conservation of mass and momentum; Navier-Stokes and Euler equations; boundary conditions; siomplified models;
Analysis: weak formulation; existence and uniqueness results for Stokes and Navier-Stokes;
Numerics: The finite element method for coercive and non-coercive problems; convergence analysis; convection-diffusion problems; stable discretization for the Stokes problem; numerical tretament of the Navier-Stokes equations;
Literature
D. Braess: Finite Elemente, Springer.
D. C. Brenner, L. R. Scott: The mathematical theory of finite element methods, Springer.
V. Girault, P.-A. Raviart: Finite Element Approximation of the Navier-Stokes Equations, Springer.
C. Johnson: Numerical solution of partial differential equations by the finite element method, Dover.
R. Temam, Navier-Stokes Equations, North-Holland Publishing.
Voraussetzungen
recommended: required: basic knowledge of partial differential equations and numerical methods
useful courses: Functional Analysis, Partial Differential Equations, Numerical Analysis of Elliptic/Parabolic Differential Equations
- Lehrende: Herbert Egger
Semester: ST 2021