HYperbolic and Kinetic Equations :
Asymptotics, Numerics, Analysis
of the




HYKE numerical gallery


Short presentation of the team G1

Sites of G1 FORTH Heraklion + Crete, Samos
URL http://www.tem.uoc.gr/~hyke/index.html
Team Organizer A. Tzavaras

The FORTH team consists of researchers of the Institute of Applied and Computational Mathematics. Many have permanent appointments in the University of Crete while others hold positions in US Universities (Brown, Texas, Wisconsin) but have a longtime participation in FORTH through affiliate appointments. The research interests of the group are in Theoretical Mechanics, Theory of Conservation Laws, Theory of Hamilton-Jacobi equations, and development of modeling and computational methods for these problems. 
The inclusion of H. M. Soner, who came back to Europe recently from the US, is on purely scientific collaboration without EU funding.

The group has extensive experience in the theory of conservation laws and Hamilton-Jacobi equations and the interface of hyperbolic and kinetic problems, with ongoing collaborations with the teams (F1, F2, F3, I1, I2). In this venue the group plans to contribute on tasks 111 , 12 and 13 , through studies of interface of kinetic and hyperbolic problems, BV theory for conservation laws, stochastic conservation laws, structure of multi-d models in elastodynamics and viscoelasticity, and kinetic formulation for systems of conservation laws and Hamilton-Jacobi equations.

Geometrical optics (task 13 ) is a topic of major interest, considered from both the viewpoint of kinetic modeling as well as via Lagrangian integrals. The Institute has a strong research experience in applications to to underwater acoustics, through participation to a number of technology oriented projects. In this direction there will be collaboration with the teams (A1, F1, F2) working on kinetic modeling and the teams (F1, F3) working on nonlinear geometrical optics. We will address problems arising from computation of high frequency densities around caustics and study eikonal Hamilton-Jacobi equations with discontinuous Hamiltonians, that are relevant in geometrical optics.

The FORTH group has an ongoing interest and collective experience on numerical methods (tasks 15 , 16 ), mainly in Finite Elements and Finite Volumes. We plan to collaborate with the teams A1, F2, D1, D2, E1 and S2 to further develop this subject, as finite elements allow great flexibility in the construction of meshes and the selection of approximation spaces. There are collaborations with the teams F2, S2 on issues related to convergence and properties of finite difference and finite volume schemes, the kinetic formulation of classical schemes, and numerical approximations of stochastic equations. A main numerical task will be the computation of complex flows with emphasis on: discontinuous elements, a posteriori estimation and adaptivity, domain decomposition and multigrid, blood and arterial flow applications.

The key scientific staff consists of


- A. Tzavaras (TO, SC) (U. Crete & U. Wisconsin, 30%)  - S. Filippas (U. Crete, 25%)  - G. Kossioris (U. Crete, 30%)  - Ch. Makridakis (TC) (U. Crete, 30%)  - D. Manoussaki (U. Crete, 25%)  - G. Makrakis (IACM-FORTH, 30%)  - C. Dafermos (IACM-FORTH & Brown, 25%)  - P. Souganidis (SAB) (IACM-FORTH & U. Texas, 25%)  - G. Zouraris (U. Aegean, 30%)  - H.M. Soner (Istanbul, external consultant, without EU funding)


[1] C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics , Grundlehren der Mathematischen Wissenschaften, 325. Springer-Verlag, Berlin, 2000.

[2] B. Perthame (F2) and P.E. Souganidis (G1), A limiting case for velocity averaging , Ann.Scient.Ecole Normale Superieure 31 (1998), 591--598.

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