Buchbeiträge:
M. Feischl, T. Führer, G. Gantner, A. Haberl, D. Praetorius:
"Adaptive boundary element methods for optimal convergence of point errors";
in: "ASC Report 34/2014",
herausgegeben von: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2014,
ISBN: 978-3-902627-07-0,
S. 1
- 22.
Kurzfassung englisch:
One particular strength of the boundary element method is that it allows for a high-order
pointwise approximation of the solution of the related partial differential equation via the
representation formula. However, the high-order convergence and hence accuracy
usually suffers from singularities of the Cauchy data. We propose two adaptive
mesh-refining algorithms and prove their quasi-optimal convergence behavior with
respect to the point error in the representation formula. Numerical examples for the
weakly-singular integral equations for the 2D and 3D Laplacian underline our theoretical
findings.
Schlagworte:
adaptive boundary element method, optimal convergence rates, point error, goal-oriented algorithm.
Elektronische Version der Publikation:
http://www.asc.tuwien.ac.at/preprint/2014/asc34x2014.pdf
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.