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Locally discontinuous but globally continuous Galerkin methods for elliptic problems

机译:椭圆问题的局部不连续但全局连续的Galerkin方法

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摘要

We propose and analyze a stabilized hybrid finite element method for elliptic problems consisting of locally discontinuous Galerkin problems in the primal variable coupled to a globally continuous problem in the multiplier. Numerical analysis shows that the proposed formulation preserves the main properties of the associate DG method such as consistency, stability, boundedness and optimal rates of convergence in the energy norm, and in the L~2(Ω) norm for adjoint consistent formulations. For using an element based data structure, it has basically the same complexity and computational cost of classical conforming finite element methods. Convergence studies confirm the optimal rates of convergence predicted by the numerical analysis presented here, with accuracy equivalent or even better than the corresponding DG approximations.
机译:我们提出并分析一种椭圆问题的稳定混合有限元方法,该方法由原始变量中的局部不连续Galerkin问题与乘数中的全局连续问题组成。数值分析表明,所提出的公式保留了相关DG方法的主要属性,如能量范数以及伴随一致公式的L〜2(Ω)范式的一致性,稳定性,有界性和最优收敛速度。对于使用基于元素的数据结构,它具有与经典一致有限元方法基本相同的复杂度和计算成本。收敛性研究证实了本文介绍的数值分析所预测的最优收敛率,其准确性与相应的DG近似值相当甚至更高。

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