椭圆边值问题等参数有限元离散化的最优$W^{1,\infty}$ -估计

ETNA - Electronic Transactions on Numerical Analysis Pub Date : 1900-01-01 DOI:10.1553/etna_vol58s1

Benjamin Dörich, Jan Leibold, B. Maier

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引用次数: 2

摘要

．考虑正则边界域上的椭圆型边值问题，用k≥1阶等参有限元将其离散化。给出了等参有限元解在w1，∞范数下的最优收敛阶。作为中间步骤，我们得到了(广义)Ritz映射的最优阶k的稳定性和收敛性估计。

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Optimal $W^{1,\infty}$-estimates for an isoparametric finite element discretization of elliptic boundary value problems

. We consider an elliptic boundary value problem on a domain with regular boundary and discretize it with isoparametric ﬁnite elements of order k ≥ 1 . We show optimal order of convergence of the isoparametric ﬁnite element solution in the W 1 , ∞ -norm. As an intermediate step, we derive stability and convergence estimates of optimal order k for a (generalized) Ritz map.

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ETNA - Electronic Transactions on Numerical Analysis

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