Local inverse estimates for non-local boundary integral operators

Abstract:

We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded Lipschitz domain $\Omega$ in $\mathbb {R}^d$ for $d\ge 2$ with piecewise smooth boundary. For piecewise polynomial ansatz spaces and $d \in \{2,3\}$, the inverse estimates are explicit in both the local mesh width and the approximation order. An application to efficiency-type estimates in a posteriori error estimation in boundary element methods is given.