奇异参数化域上同几何函数空间的逼近性质
Approximation properties of isogeometric function spaces on singularly parameterized domains
AI总结：
本文研究了奇异参数化域上同几何函数空间的逼近误差界，通过定义满足正则性条件的函数空间，证明了该类离散化方法的最优收敛性。
摘要：
我们研究了特定类型奇异参数化域上同几何函数空间的逼近误差界。在这种情况下，同几何函数是分段有理函数与分段有理几何参数化逆函数的组合。我们考虑的是参数域中一条边被映射到物理空间中一点的域。更具体地说，在我们的配置中，奇异块来源于一个常规三角块的重新参数化。在这样的域上可以定义满足一定正则性条件的同几何函数空间，从而保证最优收敛性。本文的主要贡献是证明了之前定义的同几何离散化方法的逼近误差界。
英文摘要：
We study approximation error bounds of isogeometric function spaces on a specific type of singularly parameterized domains. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise rational geometry parameterization. We consider domains where one edge of the parameter domain is mapped onto one point in physical space. To be more precise, in our configuration the singular patch is derived from a reparameterization of a regular triangular patch. On such a domain one can define an isogeometric function space fulfilling certain regularity criteria that guarantee optimal convergence. The main contribution of this paper is to prove approximation error bounds for the previously defined class of isogeometric discretizations.
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