Error control in h- and hp-adaptive FEM for Signorini's problem
Error control in h- and hp-adaptive FEM for Signorini's problem
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针对 Signorini 问题的 h 和 hp 自适应 FEM 中的误差控制
DOI：
10.1515/jnum.2009.015
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发表时间：
2009
影响因子：
4.1
通讯作者：
A. Schröder
中科院分区：
文献类型：
--
作者：
A. Schröder
摘要 本文提出了 Signorini 问题的后验有限元误差估计。离散化基于 Haslinger 等人提出的混合变分公式。其扩展到高阶有限元。后验误差控制依赖于估计作为变分方程给出的辅助问题的离散化误差。该估计由辅助问题的离散化误差的误差界限和捕获几何误差和互补条件下的误差的一些其他项组成。得出的估计应用于 h 和 hp 自适应细化和浓缩策略。数值结果证实了理论结果的适用性。特别是，获得了最佳代数收敛率和几乎指数收敛率。
Abstract This paper presents a posteriori finite element error estimates for Signorini's problem. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. The a posteriori error control relies on estimating the discretization error of an auxiliary problem which is given as a variational equation. The estimation consists of error bounds for the discretization error of the auxiliary problem and some further terms which capture the geometrical error and the error in the complementary condition. The derived estimates are applied to h- and hp-adaptive refinement and enrichment strategies. Numerical results confirm the applicability of the theoretical findings. In particular, optimal algebraic and almost exponential convergence rates are obtained.