ABSTRACT

An ensemble of independent numerical solutions makes it possible to construct a hypersphere around an approximate solution that contains the true solution. The analysis is based on some geometry considerations, such as the triangle inequality and the measure concentration in spaces of large dimensions. As a result, a nonintrusive postprocessor providing error estimation on an ensemble of solutions can be constructed. Some numerical tests for the two-dimensional compressible Euler equations are given to demonstrate the properties of such postprocessing.

中文翻译：

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一类独立解的近似误差范数的后验估计

摘要

独立数值解的整体使围绕包含真解的近似解构造超球成为可能。该分析基于一些几何因素，例如三角形不等式和大尺寸空间中的测量浓度。结果，可以构造提供对解决方案整体进行错误估计的非侵入式后处理器。给出了二维可压缩Euler方程的一些数值测试，以证明这种后处理的性质。