ABSTRACT
In this section, we deal with the idea to couple different scales. Such multiscale problems are weakly coupled and can be nearly separated into their simpler sub-systems. We assume weakly coupled models, after semi-discretization and linearization of the partial differential equations, we deal with
∂u
∂t = Au+Bu, (2.1)
u(0) = u0, (2.2)
where u ∈ X, A,B ∈ X2, X is an appropriate Banach space with a vector and induced matrix norm || · ||. Further A,B are matrices including the boundary conditions and are derived of semi-discretization, e.g., Finite Difference, Finite Volume, and Finite Element Schemes.
