Table of Contents:
1 An introduction to a posteriori error estimation for elliptic problems
1.1 A posteriori error estimation in the energy norm
1.2 A posteriori error estimation in the $L_2$ norm
2 Mesh refinement and coarsening
2.1 Refinement algorithms for simplicial meshes
2.2 Prolongation of data during refinement
2.3 Coarsening algorithms
2.4 Restriction of data during coarsening
2.5 Storage methods for hierarchical meshes
3 Adaptive strategies
3.1 Mesh refinement strategies
3.2 Coarsening strategies
3.3 Adaptive procedures for timedependent problems
3.4 Adaptive control of the time step size
4 The classical Stefan problem
4.1 Elliptic variational inequalities and the Stefan problem
4.2 A multigrid method for elliptic variational inequalities
4.3 Nonlinear SOR solvers for the Stefan problem
4.4 Adaptive method
5 The Stefan problem with surface tension and kinetic undercooling
6 Mean Curvature Flow for Hypersurfaces in ${\bf R}^n$
6.1 Some definitions and notations for hypersurfaces
6.2 Formulation of the MCF involving the Laplace--Beltrami operator
6.3 The level set formulation of MCF and the formulation for graphs
6.4 Viscosity solutions for the level set formulation
6.5 Mean curvature flow via the Allen-Cahn equation
7 Finite element methods for the MCF level set formulation
8 Adaptive discretization of the Allen--Cahn equation
9 A parametric finite element method for MCF
10 A parametric FEM for the Stefan problem with surface tension
References