Quasi-optimal convergence of AFEM based on separate marking, Part II
Quasi-optimal convergence of AFEM based on separate marking, Part II
复制标题
基于单独标记的 AFEM 准最优收敛，第二部分
DOI：
10.1515/jnma-2015-0011
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发表时间：
2015
影响因子：
3
通讯作者：
H. Rabus
中科院分区：
文献类型：
--
作者：
H. Rabus
计算流体力学和固体力学中的各种应用促使非标准有限元法（FEM）可靠而有效的自适应算法的发展。标准的自适应有限元算法由求解、估计、标记和细化的基本步骤的迭代循环组成。对于单独的标记策略，该标准方案可以通用化。（总）误差估计量被分成体积项和误差估计量项。由于体积项独立于离散解，因此可以通过高度的局部网格细化来实现适当的数据近似。这种观察导致基于单独标记的自然自适应算法。本文第二部分证明了该方法对于线弹性纯位移问题、Stokes方程和C-Crouzeix-Raviart有限元的拟最优收敛性。证明遵循与本系列第一部分中泊松模型问题相同的一般方法。数值实验证实了最优收敛速度，并显示其灵活性。
Abstract Various applications in computational fluid dynamics and solid mechanics motivate the development of reliable and efficient adaptive algorithms for nonstandard finite element methods (FEMs). Standard adaptive finite element algorithms consist of the iterative loop of the basic steps Solve, Estimate, Mark, and Refine. For separate marking strategies, this standard scheme may be universalised. The (total) error estimator is split into a volume term and an error estimator term. Since the volume term is independent of the discrete solution, an appropriate data approximation may be realised by a high degree of local mesh refinement. This observation results in a natural adaptive algorithm based on separate marking. Its quasi-optimal convergence is proven in this second part for the pure displacement problem in linear elasticity and the Stokes equations and nonconforming Crouzeix-Raviart FEM. The proofs follow the same general methodology as for the Poisson model problem in the first part of this series. The numerical experiments confirm the optimal convergence rates and reveal its flexibility.