Mathematical foundations of adaptive isogeometric analysis
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 …
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …
Adaptive isogeometric methods with hierarchical splines: an overview
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 …
splines and present the study of its numerical properties. By following [10, 12, 11], optimal …
Rate optimality of adaptive finite element methods with respect to overall computational costs
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 …
arising discrete systems are not solved exactly. For contractive iterative solvers, we …
Efficient matrix computation for isogeometric discretizations with hierarchical B-splines in any dimension
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 …
as a useful tool in the context of isogeometric analysis. However, similar as for tensor …
Refinement algorithms for adaptive isogeometric methods with hierarchical splines
C Bracco, C Giannelli, R Vázquez - axioms, 2018 - mdpi.com
The construction of suitable mesh configurations for spline models that provide local
refinement capabilities is one of the fundamental components for the analysis and …
refinement capabilities is one of the fundamental components for the analysis and …
Rate optimal adaptive FEM with inexact solver for nonlinear operators
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 …
nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also …
A hierarchical approach to the a posteriori error estimation of isogeometric Kirchhoff plates and Kirchhoff–Love shells
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 …
partial differential equations. In particular, we propose a novel algorithm to steer an adaptive …
A posteriori error estimators for hierarchical B-spline discretizations
A Buffa, EM Garau - Mathematical Models and Methods in Applied …, 2018 - World Scientific
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 …
linear second-order elliptic problems considering hierarchical spline spaces for the Galerkin …
[HTML][HTML] Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
G Gantner, D Praetorius - Computers & Mathematics with Applications, 2022 - Elsevier
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 …
B-splines for weakly-singular boundary integral equations. We prove that the employed …
[HTML][HTML] Guaranteed error bounds and local indicators for adaptive solvers using stabilised space–time IgA approximations to parabolic problems
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 …
value problems. We deduce guaranteed and fully computable error bounds adapted to …