This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-
splines and present the study of its numerical properties. By following [10, 12, 11], optimal …

We consider adaptive finite element methods for second-order elliptic PDEs, where the
arising discrete systems are not solved exactly. For contractive iterative solvers, we …

Hierarchical B-splines, which possess the local refinement capability, have been recognized
as a useful tool in the context of isogeometric analysis. However, similar as for tensor …

The construction of suitable mesh configurations for spline models that provide local
refinement capabilities is one of the fundamental components for the analysis and …

We prove convergence with optimal algebraic rates for an adaptive finite element method for
nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also …

This work focuses on the development of a posteriori error estimates for fourth-order, elliptic,
partial differential equations. In particular, we propose a novel algorithm to steer an adaptive …

In this paper, we develop a function-based a posteriori error estimators for the solution of
linear second-order elliptic problems considering hierarchical spline spaces for the Galerkin …

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 …

The paper is concerned with space–time IgA approximations to parabolic initial–boundary
value problems. We deduce guaranteed and fully computable error bounds adapted to …