Title / Abstract
Adaptive Boundary Element Methods: Error Estimation, Convergence, and OptimalityUsually, the convergence behavior of numerical schemes is spoiled by singularities of the given data and/or the unknown solution. The purpose of a posteriori error estimation is twofold: Firstly, a posteriori error estimators allow to compute bounds on the current discretization error, secondly, the local information provided by the a posteriori error estimator can be used to adapt the discretization to possible singularities. Our talks will give a rough overview on a posteriori error estimation and related adaptive mesh-refinement for boundary element methods with a focus on convergence and quasi-optimal convergence rates. The outline of the presentation reads as follows:
Outline and References
Lecture 1: Introduction and (h-h/2)-based error estimators.S. Ferraz-Leite, D. Praetorius: Simple a posteriori error estimators for the h-version of the boundary element method, Computing, 83 (2008), 135-162.
Lecture 2: Estimator reduction principle and convergence of adaptive BEM.
M. Aurada, S. Ferraz-Leite, D. Praetorius: Estimator reduction and convergence of adaptive BEM, Appl. Numer. Math., 62 (2012), 787-801.
Lecture 3 + 4: Rate optimality of adaptive BEM.
C. Carstensen, M. Feischl, M. Page, D. Praetorius: Axioms of adaptivity, Comput. Math. Appl., 67 (2014), 1195-1253.
Lecture 5: Local inverse estimates for nonlocal operators.
M. Feischl, M. Karkulik, J. Melenk, D. Praetorius: Quasi-optimal convergence rate for an adaptive boundary element method, SIAM J. Numer. Anal., 51 (2013), 1327-1348.
Handouts
Handout Part 1 (latest update 27 Aug)Handout Part 2 (latest update 27 Aug)
Handout Part 3 (latest update 27 Aug)
Handout Part 4 (latest update 27 Aug)
Handout Part 5 (latest update 27 Aug)
Exercises
Exercises (latest update 27 Aug)Exercises with sketches (Aug 27)
