We are organizing a minisymposium on Adaptivity, Regularity and, Fast Approximation at the European Numerical Mathematics and Advanced Applications Conference 2019 (EnuMath 2019) which takes place in Egmond aan Zee (Netherlands) in September / October 2019.
Session Abstract
In recent years the enormous increase in computer power paved the way for the development of more and more complicated models of real-life phenomena which have to be analyzed and simulated. Thus, motivated by applications from natural sciences, engineering, or even finance, the efficient numerical treatment of these models has become an area of increasing importance. Many problems of this type are usually formulated in terms of (possibly nonlinear) equations involving partial differential or integral operators acting between Hilbert spaces. In practice, typical approaches towards numerical solutions (e.g., based on Galerkin formulations) might lead to systems with hundreds of thousands or even millions of unknowns. Therefore, adaptive strategies suggest themselves in order to increase efficiency. However, although numerical experiments strongly indicate that the use of adaptivity finally pays off, a sound theoretical justification still has to be developed for large classes of problems. Reaching this goal particularly requires a deep understanding of structural properties such as, e.g., regularity of the unknown solutions in various function spaces. On the other hand, elaborated a posteriori error analysis is needed in order to design efficient algorithms of adaptive finite element or wavelet type.
We aim not only to present results from established scientists but also to provide young promising researchers with a forum for their newest results.
Confirmed Speakers
- Peter Binev (University of South Carolina, USA): Near-best adaptive approximations
- Andreas Veeser (Università degli Studi di Milano, Italy): Tree approximation with conforming meshes
- Michael Feischl (TU Wien, Austria): Optimal adaptivity for the Stokes problem
- Stefan Schimanko (TU Wien, Austria): Rate optimal adaptive FEM with inexact solver for nonlinear operators
- Rob Stevenson (University of Amsterdam, The Netherlands): Adaptive methods for solving parabolic evolution equations
- Stephan Dahlke (Philipps-University of Marburg, Germany): Besov regularity of solutions to linear and nonlinear parabolic PDEs
- Toni Scharle (University of Oxford, UK): A priori regularity results for discrete solutions to elliptic equations on graded meshes
- Markus Weimar (Ruhr University Bochum, Germany): Higher order regularity shifts for the p-Poisson problem