Paper Info
Title
Convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis.
Abstract
In this paper, we present convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis. First, the approximation errors with the L2(Ω)-norm and the H1(Ω)-seminorm are estimated locally. The impact of singularities is considered in this framework. Second, the convergence rates for solving PDEs with singular parameterizations are discussed. These results are based on a weak solution space that contains all of the weak solutions of elliptic boundary value problems with smooth coefficients. For the smooth weak solutions obtained by isogeometric analysis with singular parameterizations and the finite element method, both are shown to have the optimal convergence rates. For non-smooth weak solutions, the optimal convergence rates are reached by setting proper singularities of a controllable parameterization, even though convergence rates are not optimal by finite element method, and the convergence rates by isogeometric analysis with singular parameterizations are better than the ones by the finite element method.
Year
DOI
Venue
2017
10.1016/j.cagd.2017.02.006
Computer Aided Geometric Design
Keywords
Field
DocType
Singular parameterizations,Isogeometric analysis,Elliptic boundary value problems,Approximation error estimates,Convergence rates
Convergence (routing),Boundary value problem,Mathematical optimization,Parametrization,Mathematical analysis,Isogeometric analysis,Finite element method,Weak solution,Gravitational singularity,Mathematics
Journal
Volume
ISSN
Citations 
52
0167-8396
0
PageRank 
References 
Authors
0.34
4
5
Name
Order
Citations
PageRank
Meng Wu15110.26
Yicao Wang200.34
Bernard Mourrain31074113.70
Boniface Nkonga4627.04
Changzheng Cheng500.34