#### Graduate Seminar in summer term 2015:

# S4E2 – Convergence and Optimality of Adaptive Finite Element Methods

**Requirements:** Basic knowledge in partial differential equations and finite element methods.

#### Description:

Self-adaptive discretization methods for the numerical solution of partial differential equations have gained enormous importance in many scientific and engineering applications. These methods aim to minimize the amount of work that is required to obtain a numerical solution within a prescribed tolerance. Their driving force are posteriori error estimators which are used to control the adaptive mesh refinement or, in general, the adaptive enrichment of finite element spaces.

This seminar concerns the recent algorithmic and theoretical breakthroughs in this context, this is, the convergence and optimality of adaptive finite element methods in the sense of quasi-minimal computational complexity.

The seminar will be based mainly on selected journal articles. Students interested in the seminar might contact P. Morgenstern in advance to register.

#### Literature:

[1] | C. Carstensen, M. Feischl, M. Page, and D. Praetorius. *Axioms of adaptivity*. Comput. Math. Appl., 67(6):1195–1253, 2014. |

[2] | L. Diening, C. Kreuzer, and R. Stevenson. *Instance optimality of the adaptive maximum strategy*. Foundations of Computational Mathematics, pages 1–36, 2015. |

[3] | R. Verfürth. *A posteriori error estimation techniques for finite element methods*. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, 2013. |

**Date:** | Tuesday, 14(c.t.)–16, | Wegelerstr. 6, SR 5.002 |

**First seminar meeting:** | April 7th. |