Report 37/2005: Mini-workshop: Convergence of adaptive algorithms (August 14th -- August 20th, 2005) (Q870679)

Summary: Adaptive refinement strategies are a key concept for the efficient numerical solution of partial differential equations. New findings allow the study of convergence and optimality of adaptive finite element methods. It was the aim of the Oberwolfach to discuss necessary conditions for optimal convergence and to extend the theory to new areas of application. Contributions: {\parindent=5mm \begin{itemize}\item[--]Roland Becker and Rolf Rannacher, Some Thoughts about Convergence of the DWR Method (p. 2097) \item[--]Peter Binev (joint with Wolfgang Dahmen and Ronald DeVore), Adaptive Finite Element Methods with Optimal Complexity (p. 2101) \item[--]Carsten Carstensen, Survey on the Convergence of Adaptive Finite Element Methods (p. 2104) \item[--]Leszek Demkowicz (joint with Jason Kurtz, David Pardo), Automatic \(hp\)-Adaptivity. A Progress Report (p. 2111) \item[--]Willy Dörfler, Vincent Heuveline, Convergence of an Adaptive \(hp\)-Finite Element Method (p. 2116) \item[--]Ronald H.W. Hoppe (joint with Carsten Carstensen), Convergence Analysis of Adaptive Mixed and Nonconforming Finite Element Methods (p. 2120) \item[--]Markus Melenk (joint with Tino Eibner, Barbara Wohlmuth), On Adaptivity in hp-FEM (p. 2122) \item[--]Pedro Morin (joint with Khamron Mekchay, Ricardo H. Nochetto) \item[--]A Convergent Adaptive Algorithm for the Laplace-Beltrami Operator (p. 2126) \item[--]Kunibert G. Siebert (joint with Andreas Veeser), Convergence of the Equidistribution Strategy (p. 2129) \item[--]Rob Stevenson, Optimal Adaptive Finite Element Methods without Coarsening (p. 2131) \item[--]Andreas Veeser (joint with Kunibert G. Siebert), Convergent adaptive finite elements for rough and conforming obstacles (p. 2133) \end{itemize}}