Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
Provides a rigorous convergence proof for adaptive IGA BEM, addressing a known gap in the theoretical foundation for practitioners in computational engineering.
The paper proves that an adaptive isogeometric boundary element method for weakly-singular integral equations converges with optimal algebraic rates, extending prior work on error estimation.
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.