Effective laws for the Poisson equation on domains with curved oscillating boundaries
Nicolas Neuß, Maria Neuss‐Radu, Andro Mikelić · Applicable Analysis · 2005
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.