Quantifying the error that is induced by numerical approximation techniques is an important task in many fields of applied mathematics. Two characteristic properties of error bounds that are desirable are reliability and efficiency. In this article, we present an error estimation procedure for general nonlinear problems and, in particular, for parameter-dependent problems. With the presented auxiliary linear problem (ALP)-based error bounds and corresponding theoretical results, we can prove large improvements in the accuracy of the error predictions compared with existing error bounds. The application of the procedure in parametric model order reduction setting provides a particularly interesting setup, which is why we focus on the application in the reduced basis framework. Several numerical examples illustrate the performance and accuracy of the proposed method.

中文翻译：

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非线性问题的严格有效后验误差界—在RB方法中的应用

量化由数值逼近技术引起的误差是许多应用数学领域的重要任务。期望的误差界限的两个特征是可靠性和效率。在本文中，我们提出了一种针对一般非线性问题，尤其是与参数有关的问题的误差估计程序。借助提出的基于辅助线性问题（ALP）的误差范围和相应的理论结果，我们可以证明与现有误差范围相比，误差预测的准确性有较大的提高。该过程在参数模型降阶设置中的应用提供了特别有趣的设置，这就是为什么我们专注于简化基础框架中的应用的原因。