Abstract: In dissipative phenomena energy is lost as time evolves, no matter how much energy may have been at an initial state. In those dissipative phenomena modelled by partial differential equations (PDEs), dissipation implies that trajectories enter a compact set in finite time and do not scape from it. This has led to the development of new ideas to better capture and understand the long term dynamics of dissipative phenomena. Among those are inertial manifolds (IMs), which are finite-dimensional manifolds that attract all other orbits exponentially. Since very few PDEs have been shown to possess an IM, the concept of approximate inertial manifold has been introduced, leading to novel numerical method such as the nonlinear Galerkin Method.
Recent work shows that Nonlinear Galerkin methods may no result efficient in practice due to their high computational cost. In the present proposal, we intend to develop efficient methods that take advantage of AIMs but without paying the price of nonlinear Galerkin methods, such as the recently introduced postprocessed Gakerkin method.
Source of Funding: Promoción general del conocimiento DGICYT (PB95-0216) (General promotion of Knowledge)
Implied entities: Universidad Autónoma de Madrid
iMAT research line: RL7: Numerical Analysis
