Description of the Lecture Series
The purpose of the keynote lectures is to give an overview over
current a posteriori error estimation techniques, related mesh
adaptation strategies and their application to problems in
Computational Science and Engineering. They will be targeted at an
audience with basic knowledge of the finite element method, as for
instance the key chapters of the books
by Braess,
Brenner
and Scott, Carey and
Oden, Ciarlet
or Strang and Fix. The topics will cover material on adaptivity and a
posteriori error estimation
(see Bangerth
and Rannacher).
The ten lectures of this conference will center around the following areas:
- Basic concepts: Variational form of partial
differential equations; finite element approximation; a priori
versus a posteriori error analysis; Galerkin orthogonality and
duality arguments; residual-based a posteriori error estimates;
reliability and efficiency of error estimates.
- Adaptive mesh refinement strategies: Local error
indicators; strategies for mesh adaptation; hanging nodes and
transition elements; optimal mesh refinement; feature-based versus
residual-based mesh adaptation.
- Goal-oriented error estimation: The dual weighted
residual (DWR) method; examples of functional estimates; evaluation
of error estimators; practical aspects; illustrative examples.
- Time-dependent problems: The DG method for time
discretization; the nonstationary dual problem; efficient
computation of dual solutions; evaluation of error estimators;
sample applications: heat and wave equation.
- Nonlinear problems: Derivation of estimates for
nonlinear problems; augmentation of nonlinear iteration for the dual
problem; application to the incompressible Navier-Stokes equations.
- Applications I: Application of the DWR technique to
technical flow problems; Euler and Navier-Stokes equations;
numerical stabilization; drag and lift computation.
- Applications II: Application of the DWR technique to
coupled systems; chemically reactive flows; fluid-structure interaction
problems.
- Eigenvalue problems: Finite element approximation of
eigenvalue problems; the eigenvalue problems as a coupled nonlinear
system; a priori and a posteriori error estimates for eigenvalues;
application to stability analysis of stationary flow.
- Optimization: Optimal control and parameter estimation
problems; derivation of the dual problem; tracking-type problems;
discrete parameter estimation; sample applications.
- Applications III: Parameter estimation and model
calibration for chemically reactive flow; problems with control and
state-constraints.
Back to 2009 CBMS Conference on Adaptive Finite Element Methods.