Primer of Adaptive Finite Element Methods
Primer of Adaptive Finite Element Methods
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自适应有限元方法入门
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Veeser
中科院分区：
文献类型：
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作者：
R. Nochetto;A. Veeser
自适应有限元方法是科学和工程中求解偏微分方程的基本数值方法。在20世纪80年代和90年代大量的effortwas致力于设计的后验误差估计，以下的开创性工作巴布？斯卡。这些是可计算的量，取决于离散解和数据，可用于评估近似质量并自适应地改进它。尽管他们的实际成功，自适应过程已被证明是收敛的，并表现出最佳的基数，只是最近的维数d > 1和线性椭圆偏微分方程。这一系列讲座介绍了AFEM的最新讨论，包括残差型估计量的上、下后验误差界的推导，包括对振荡作用的批判性审视，AFEM的设计及其基本性质，以及对AFEM的收敛性、收缩性和准最优基数的完整讨论
Adaptive finite element methods (AFEM) are a fundamental numerical instrument in science and engineering to approximate partial differential equations. In the 1980s and 1990s a great deal of effortwas devoted to the design of a posteriori error estimators, following the pioneering work of Babu?ska. These are computable quantities, depending on the discrete solution(s) and data, that can be used to assess the approximation quality and improve it adaptively. Despite their practical success, adaptive processes have been shown to converge, and to exhibit optimal cardinality, only recently for dimension d > 1 and for linear elliptic PDE. These series of lectures presents an up-to-date discussion of AFEM encompassing the derivation of upper and lower a posteriori error bounds for residual-type estimators, including a critical look at the role of oscillation, the design of AFEM and its basic properties, as well as a complete discussion of convergence, contraction property and quasi- optimal cardinality of AFEM