Optimized interface conditions in domain decomposition methods to solve reaction-diffusion problems with strong heterogeneity in the coefficients in a sectorial domain

The aim of this paper is to derive appropriate second order transmission boundary conditions near the corner used in domain decomposition methods to study the reaction-diffusion problems (“−∇.(ν(x)∇.)+η(x).”) with strong heterogeneity in the coefficients in a singular non-convex domain with Neumann and Dirichlet boundary condition. These transmission conditions will be tested and compared numerically with other approaches.