A multiscale model reduction method for partial differential equations (Q2877386)

A multiscale model reduction method for several standard types of elliptic, parabolic, hyperbolic and convection-diffusion equations is presented. An essential ingredient of the method is to decompose the harmonic coordinates into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Such a decomposition plays a key role in the construction of the effective equation. The solution to the effective equation is in \(H^2\) and can be approximated by a regular coarse mesh and it is easy to implement. Another advantage of this approach is that it does not require scale separation of periodic structures as traditional homogenization theory.