Analysis of Discontinuous Galerkin IGA Approximations to Elliptic Boundary Value Problems
Analysis of Discontinuous Galerkin IGA Approximations to Elliptic Boundary Value Problems
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发表时间：
2014
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通讯作者：
U. Langer;I. Toulopoulos
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作者：
U. Langer;I. Toulopoulos
在这项工作中，我们研究了一种新的方法的逼近性能，应用等几何分析（伊加）离散化的概念和间断Galerkin技术的接口，解决线性扩散与间断扩散系数。该算法将计算域划分为互不重叠的子区域，在伊加中称为分片，在分片中构造B-Spline有限维近似空间。问题的解在每个子域中近似，而不施加任何匹配网格条件，并且对界面上的离散解没有任何连续性要求。为了处理离散解在界面上的不连续性，采用了带内罚跳跃项的数值通量。本文给出了二维和三维区域中问题的先验误差分析，其解属于W，l ≥ 2，p ∈（2d d+2（l−1），2].在任何情况下，我们显示最佳的收敛速度的离散化方面的。
In this work, we study the approximation properties of a new method, that applies the Isogeometric Analysis (IGA) discretization concept and the Discontinuous Galerkin technique on the interfaces, for solving linear diffusion with discontinuous diffusion coefficients. The computational domain is divided into non-overlapping sub-domains, called patches in IGA, where B−Spline finite dimensional approximations spaces are constructed. The solution of the problem is approximated in every sub-domain without imposing any matching grid conditions and without any continuity requirements for the discrete solution on the interfaces. Numerical fluxes with interior penalty jump terms are applied in order to treat the discontinuities of the discrete solution on the interfaces. We present an a priori error analysis for problems set in twoand threedimensional domains, with solutions belonging to W , l ≥ 2, p ∈ ( 2d d+2(l−1) , 2]. In any case, we show optimal convergence rates of the discretization with respect to ‖.‖DG-norm.