SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Plenary Lecture


From Darcy to wave equations: a few examples of numerical homogenization

A. Abdulle

Abstract
Starting with the famous constitutive law for the flow of a fluid through a column of sand proposed by Henry Darcy in the mid 19th century, we will discuss the various scales hidden in such a physical process and briefly introduce the notion of homogenization. We will then present recent developments in the design and analysis of numerical homogenization methods. The emphasize will be on multiscale problems, where the fine scale equation and the effective equation are not of the same type. In particular, numerical methods that couple Stokes and Darcy problems and numerical methods for capturing wave propagation in heterogeneous media over long time.

Bibliography
[1] A. Abdulle and Y. Bai. Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems, J. Comput. Phys., vol. 191, num. 1, p. 18-39, 2012.
[2] A. Abdulle, M. J. Grote and C. Stohrer. FE heterogeneous multiscale method for long time wave propagation, C. R. Math. Acad. Sci. Paris, vol. 351, p. 495-499, 2013.
[3] A. Abdulle and G. Vilmart. Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, to appear in Math. Comp.
[4] A. Abdulle and M.E. Huber. Discontinuous Galerkin finite element heterogeneous multiscale method for advection–diffusion problems with multiple scales, to appear in Numer. Math.

Organized by         Universidad de Valladolid     IMUVA