迹和通量先验误差估计在Signorini型问题有限元近似中的应用
Trace and flux a priori error estimates in finite element approximations of Signorni-type problems
AI总结：
本文基于Signorini问题，提出新的最优阶先验误差估计，通过精确的Steklov-Poincaré算子和对偶性论证，分析迹和通量在Signorini边界上的误差。
摘要：
变分不等式在许多应用中起重要作用，是活跃的研究领域。自然能量范数中存在最优的先验误差估计，但其他范数中的结果很少。本文以简单的Signorini问题为例，提供迹和通量在Signorini边界上的新最优阶先验误差估计。先验分析基于精确的Steklov-Poincaré算子和依赖于网格的算子，以及Aubin-Nitsche类型的对偶性论证。数值结果展示了有限元方法的收敛率。
英文摘要：
Variational inequalities play in many applications an important role and are an active research area. Optimal a priori error estimates in the natural energy norm do exist but only very few results in other norms exist. Here we consider as prototype a simple Signorini problem and provide new optimal order a priori error estimates for the trace and the flux on the Signorini boundary. The a priori analysis is based on the exact and a mesh-dependent Steklov-Poincaré operator as well as on duality in Aubin-Nitsche type arguments. Numerical results illustrate the convergence rates of the finite element approach.
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