Elliptic reconstruction property, originally introduced by Makridakis and Nochetto for linear parabolic problems, is a well-known tool to derive optimal a posteriori error estimates. No such results are known for nonlinear and nonsmooth problems such as parabolic variational inequalities (VIs). This article establishes the elliptic reconstruction property for parabolic VIs and derives a posteriori error estimates in $L^{\infty}(0,T;L^{2}(\Omega))$. The estimator consists of discrete complementarity terms and standard residual. As an application, the residual-type error estimates are presented.

翻译：椭圆重构性质最初由Makridakis和Nochetto针对线性抛物问题提出，是推导最优后验误差估计的经典工具。对于抛物型变分不等式这类非线性和非光滑问题，尚未见类似结果。本文建立了抛物型变分不等式的椭圆重构性质，并推导了$L^{\infty}(0,T;L^{2}(\Omega))$空间中的后验误差估计。该估计量包含离散互补项与标准残差项。作为应用，本文给出了残差型误差估计。