Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations

TL;DR

This paper develops an adaptive isogeometric boundary element method using hierarchical B-splines for weakly-singular integral equations, proving reliability and optimal convergence, with numerical validation for 3D Poisson and elasticity problems.

Contribution

It introduces a new adaptive algorithm with hierarchical B-splines for boundary integral equations, demonstrating reliability and optimal convergence rates.

Findings

Error estimator is reliable and converges optimally.

Numerical experiments confirm theoretical convergence.

Method applies to general elliptic systems like elasticity.

Abstract

We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed weighted-residual error estimator is reliable and converges at optimal algebraic rate. Numerical experiments with isogeometric boundary elements for the 3D Poisson problem confirm the theoretical results, which also cover general elliptic systems like linear elasticity.