Lunari, Andrea: Numerics and optimal control of phase-field models for multiphase flow. 2018
Inhalt
- 1 Introduction
- 2 Optimal Control of the Non-Smooth Cahn-Hilliard-Stokes System
- 2.1 Introduction
- 2.2 Regularized Optimal Control Problem
- 2.2.1 Properties of the Regularized State Equations
- 2.2.2 Well-Posedness of the Regularized Optimal Control Problem
- 2.2.3 Optimality Conditions of the Regularized Optimal Control Problem
- 2.3 Non-Smooth Optimal Control Problem
- 3 Optimal Control of the Discrete Non-Smooth Cahn-Hilliard-Stokes System
- 3.1 Introduction
- 3.2 Regularized Discrete Optimal Control Problem
- 3.2.1 Properties of the Regularized Discrete State Equations
- 3.2.2 Well-Posedness of the Regularized Discrete Optimal Control Problem
- 3.2.3 Optimality Conditions for the Regularized Discrete Optimal Control Problem
- 3.3 Discrete Non-Smooth Optimal Control Problem
- 3.3.1 Properties of the State Equations of the Discrete Non-Smooth Optimal Control Problem
- 3.3.2 Minimizers of the Discrete Non-Smooth Optimal Control Problem
- 3.3.3 Optimality Conditions for the Discrete Non-Smooth Optimal Control Problem
- 3.4 Convergence of the Solutions of the Discrete Optimal Control Problem
- 3.5 Numerical Solution of the Discrete Optimal Control Problem
- 3.6 Numerical Experiments
- 4 Optimal Control of the Cahn-Hilliard-Navier-Stokes System
- 4.1 Introduction
- 4.2 Properties of the State Equations
- 4.3 Well-Posedness of the Optimal Control Problem
- 4.4 Optimality Conditions of the Optimal Control Problem
- 5 Optimal Control of the Discrete Cahn-Hilliard-Navier-Stokes System
- 5.1 Introduction
- 5.2 Properties of the Discrete State Equations
- 5.3 Well-Posedness of the Discrete Optimal Control Problem
- 5.4 Optimality Conditions for the Discrete Optimal Control Problem
- 5.5 Convergence of the Solutions of the Discrete Optimal Control Problem
- 5.6 Numerical Solution of the Discrete Optimal Control Problem
- 5.7 Numerical Experiments
- A Notations and Basic Results
- A.1 Main Notations
- A.2 Banach Spaces
- A.2.1 General Notation
- A.2.2 Sobolev and Bochner spaces
- A.2.3 Useful Embeddings
- A.2.4 Useful Inequalities
- A.2.5 Green's Operator
- A.3 Discrete Settings
- B Proofs
- Bibliography