Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and error indicators that show distributions of global and local errors of a particular numerical solution. In this paper, we focus on a particular class of domain decomposition methods (DDM), which are among the most efficient numerical methods for solving PDEs. We adapt functional type a posteriori error estimates and construct a special form of error majorant which allows efficient error control of approximations computed via these DDM by performing only subdomain-wise computations. The presented guaranteed error bounds use an extended set of admissible fluxes which arise naturally in DDM.
翻译:目前,后遗错误控制方法已成为数字分析中一个新的重要部分。 其宗旨是获取各种规范和错误指标中的可计算错误估计值, 这些规范和错误指标显示特定数字解决方案的全球和地方错误分布情况。 在本文中, 我们侧重于特定类别的域分解方法( DDM ), 这是解决 PDE 的最有效的数字方法之一。 我们调整了功能型的后遗错误估计值, 并构建了一种特殊的错误主要形式, 使通过这些 DDM 计算出的近似值能够有效地控制误差, 只需进行子DDM 的计算。 提供的保证错误约束使用一系列在 DDM 中自然产生的可接受通量。