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.

功能误差估计是用于后验误差估计和有限元方法（FEM）的相关自适应网格细化的成熟工具。本工作提出了边界元法（BEM）的第一个功能误差估计。一个关键特征是，得出的误差估计与BEM离散化无关，并为未知误差提供了有保证的上下限。特别是，我们的分析涵盖了Galerkin BEM和搭配方法，这使得该方法对于科学计算和工程应用尤为重要。拉普拉斯问题的数值实验证实了理论结果。