Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations. (1st July 2022)

• Record Type: Journal Article
• Authors: Gantner, Gregor; Praetorius, Dirk
• Is Part Of: Computers & mathematics with applications. Volume 117(2022)
• Page Start: 74
• Page End: 96
• Publication Date: 2022-07-01
• Subjects: Boundary element method -- Isogeometric analysis -- Hierarchical splines -- Adaptivity -- Optimal convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.04.006
• Languages: English
• ISSNs: 0898-1221

Abstract

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.