Adaptive 2D IGA boundary element methods
arXiv:1504.06164 · doi:10.1016/j.enganabound.2015.10.003
Abstract
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error estimator for Galerkin IGA boundary element methods, the present work focuses more on collocation and weighted- residual error estimators, which provide reliable upper bounds for the energy error. Our analysis allows piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. We formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments show that the proposed adaptive strategy leads to optimal convergence, and related IGA boundary element methods are superior to standard boundary element methods with piecewise polynomials.
arXiv admin note: text overlap with arXiv:1408.2693
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- A study on spline quasi-interpolation based quadrature rules for the isogeometric Galerkin BEM
- Adaptive IGAFEM with optimal convergence rates: T-splines
- Adaptive isogeometric boundary element methods with local smoothness control
- Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
- Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
- Stable implementation of adaptive IGABEM in 2D in MATLAB
- Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations