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arXiv · 1601.07244

Isogeometric Least-squares Collocation Method with Consistency and Convergence Analysis

Hongwei Lin·Yunyang Xiong·Xiao Wang·Qianqian Hu
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Abstract

In this paper, we present the isogeometric least-squares collocation (IGA-L) method, which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense. The number of collocation points employed in IGA-L can be larger than that of the unknowns. Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods. First, a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution. Second, IGA-L method is more flexible and more stable, because the number of collocation points in IGA-L is variable. Third, IGA-L is convergent in some cases of singular parameterization. Moreover, the consistency and convergence analysis are also developed in this paper.

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Hongwei Lin, Yunyang Xiong, Xiao Wang, Qianqian Hu. 2016-01-27. Isogeometric Least-squares Collocation Method with Consistency and Convergence Analysis. https://arxiv.org/abs/1601.07244

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