Contributions to Books:
M. Feischl, G. Gantner, D. Praetorius:
"Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations";
in: "ASC Report 23/2014",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D.
We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS.
In particular, our analysis gives a first contribution to adaptive BEM in the frame of isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots.
Numerical experiments underline the theoretical findings and show that the proposed adaptive strategy leads to optimal convergence.
isogeometric analysis, boundary element method, a posteriori error estimate, adaptive mesh-refinement.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.