抽象框架中第二类变分不等式的后验误差估计
A posteriori error estimates for variational inequalities of the second kind in an abstract framework
AI总结：
本文提出一个抽象框架，用于推导第二类变分不等式的可靠且局部有效的后验误差估计子，并通过摩擦接触和Mosolov型问题的数值实验验证其广泛适用性。
AI中文摘要：
本文引入了一个抽象框架，用于推导第二类变分不等式的可靠后验误差估计子。在某些条件下，还可以推导出误差估计子的（局部）有效性。该框架基于对残差的估计，该残差源于一个等价的混合公式，以及用（可能经过后处理的）离散对应量替换拉格朗日乘子。该方法被应用于一个理想化的摩擦接触问题和一个Mosolov型模型问题，采用$hp$-有限元离散化设置。多个数值实验证明了理论发现的广泛适用性。
英文摘要：
In this paper, an abstract framework is introduced for the derivation of reliable a posteriori error estimators for variational inequalities of the second kind. Under certain conditions (local) efficiency of the error estimators can also be derived. The framework is based on the estimation of a residuum which results from an equivalent mixed formulation and from the replacement of the Lagrange multiplier by its (possibly post-processed) discrete counterpart. The approach is applied to an idealized frictional contact problem and a Mosolov type model problem in an $hp$-finite element discretization setup. Several numerical experiments demonstrate the broad applicability of the theoretical findings.
