Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
arXiv:1510.05111 · doi:10.1007/s00211-016-0836-8
Abstract
In a recent work, we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms.
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Cited by in corpus (12)
- Mathematical foundations of adaptive isogeometric analysis
- A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling
- Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
- An adaptive IGA-BEM with hierarchical B-splines based on quasi-interpolation quadrature schemes
- Adaptive BEM with optimal convergence rates for the Helmholtz equation
- 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
- Isoparametric singularity extraction technique for 3D potential problems in BEM
- Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations