# FRB

## Seminar

### Numerical Methods for FBPs - 4

Seminar Room 1, Newton Institute

#### Abstract

This 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.

#### Video

**The video for this talk should appear here if JavaScript is enabled.**

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.