We build up a decomposition for the flow generated by heat equation with real analytic memory kernel. It consists of three components: The first one is parabolic nature; second gathers hyperbolic component dynamics, null velocity propagation; last exhibits finite smoothing effect. This reveals hybrid parabolic-hyperbolic nature and clearly illustrates significant impact term on behavior system ...

We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the two subdomains. In particular, in one subdomain we discretize the governing equations by a canonical scheme, whereas in the other one we solve a reduced ord...

This report explores some numerical alternatives that can be exploited to derive efficient low-order models of the Navier-Stokes equations. It is shown that an optimal solution sampling can be derived using appropriate norms of the Navier-Stokes residuals. Then the classical Galerkin approach is derived in the context of a residual minimization method that is similar to variational multiscale m...