Numerical Methods for FBPs - 1
Seminar Room 1, Newton Institute
AbstractThis tutorial is a tour from classical techniques to recent developments of numerical methods for free boundary problems. The emphasis is on ideas and methods rather than problems.
Lecture 1: Variational Inequalities I
The classical obstacle problem. A priori error analysis in energy and maximum norm. The thin obstacle problem. The fractional obstacle problem.
Lecture 2: Variational Inequalities II
A priori rate of convergence for free boundaries. A posteriori error analysis in the maximum norm. A posteriori barrier sets.
Lecture 3: Discrete Gradient Flows
Evolution PDE: energy solutions, convexity, coercivity. Error analysis of time discretization. Error analysis of space discretization. Applications: parabolic variational inequalities, degenerate parabolic PDE, TV gradient flow.
Lecture 4: Geometric Problems
Shape differential calculus: examples. Geometric gradient flows: mean curvature, surface diffusion, Willmore flow. Parametric approach. Phase field approach. Level set approach.
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