Streamline upwind/Petrov–Galerkin-based stabilization of proper generalized decompositions for high-dimensional advection–diffusion equations


Correspondence to: Elías Cueto, Universidad de Zaragoza. Edificio Betancourt. María de Luna, s.n. E-50018 Zaragoza, Spain.



This work is a first attempt to address efficient stabilizations of high dimensional advection–diffusion models encountered in computational physics. When addressing multidimensional models, the use of mesh-based discretization fails because the exponential increase of the number of degrees of freedom related to a multidimensional mesh or grid, and alternative discretization strategies are needed. Separated representations involved in the so-called proper generalized decomposition method are an efficient alternative as proven in our former works; however, the issue related to efficient stabilizations of multidimensional advection–diffusion equations has never been addressed to our knowledge. Thus, this work is aimed at extending some well-experienced stabilization strategies widely used in the solution of 1D, 2D, or 3D advection–diffusion models to models defined in high-dimensional spaces, sometimes involving tens of coordinates.Copyright © 2013 John Wiley & Sons, Ltd.