Abstract
In this article, we derive approximations and effective boundary laws for solutions u
∊ of the Poisson equation on a domain whose boundary differs from the smooth boundary of a domain
by rapid oscillations of size ε. We construct a boundary layer correction which yields an O(ε) approximation in the energy norm and an
approximation in the L
2-norm for a right-hand side
. We also show that the same approximation order can be obtained for the error on subdomains by solving an effective equation on Ω satisfying a boundary condition of Robin type.
Notes
†Note that for c bl >0, problem (Equation99) can be ill-posed without further restictions on ∊ and cbl .