Adaptive IGAFEM with optimal convergence rates: T-splines
arXiv:1910.01311 · doi:10.1016/j.cagd.2020.101906
Abstract
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of [Morgenstern, Peterseim, Comput. Aided Geom. Design 34 (2015)] in 2D and [Morgenstern, SIAM J. Numer. Anal. 54 (2016)] in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (which is equivalent to the sum of energy error plus data oscillations) with optimal algebraic rates with respect to the number of elements of the underlying mesh.
arXiv commentarXiv admin note: text overlap with arXiv:1701.07764
References in corpus (13)
- Axioms of Adaptivity
- Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems
- Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison
- Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems
- Analysis-suitable adaptive T-mesh refinement with linear complexity
- Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations
- Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
- Adaptive 2D IGA boundary element methods
- Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
- Globally structured 3D Analysis-suitable T-splines: definition, linear independence and m-graded local refinement
- Adaptive BEM with inexact PCG solver yields almost optimal computational costs
- BPX preconditioners for isogeometric analysis using analysis-suitable T-splines
- Adaptive isogeometric boundary element methods with local smoothness control
Cited by in corpus (5)
- Mathematical foundations of adaptive isogeometric analysis
- Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
- Stable implementation of adaptive IGABEM in 2D in MATLAB
- Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations
- Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis