Error estimates of high-order difference schemes for elliptic equations with intersecting interfaces

In the work \cite{Ang} high-order difference schemes (numerical experiments show second and fourth order of convergence) were derived, but with 1-st and 3-d order local truncation error, respectively, compact difference schemes for elliptic equations with intersecting interfaces. Here, for these difference schemes, we provide error estimates in discrete Sobolev norms.