Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.

翻译：功能错误估计是事后误差估计和相关有限元素法的适应性网格改进的既定工具。本项工作为边界元素法提出了第一个功能错误估计。一个关键特征是,产生的误差估计独立于BEM离散,为未知错误提供保证的下限和上界。特别是,我们的分析涉及Galerkin BEM和合用法,这是科学计算和工程应用中特别感兴趣的方法。Laplace问题的数字实验证实了理论结果。