Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations

Abstract

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.

References in corpus (3)

• Axioms of Adaptivity
• ZZ-type aposteriori error estimators for adaptive boundary element methods on a curve
• Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without h-weighting factor

Cited by in corpus (14)

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• Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
• Adaptive BEM with optimal convergence rates for the Helmholtz equation
• 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