HYperbolic and Kinetic Equations :
Asymptotics, Numerics, Analysis
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Short presentation of the team S2

Sites of S2 KTH Stockholm + Lund, Trondheim, Oslo, Bergen
URL http://www.nada.kth.se/~szepessy/S2_HYKE.html
Team Organizer A. Szepessy

The research activities in our team cover the whole spectrum from theory of ordinary and partial differential equations, including also stochastics, to applications. The theoretical emphasis is on nonlinear conservation laws and the Navier-Stokes equations, and on problems with several scales, e.g., in computational electromagnetics and multi phase flow in porous media. The applications are pursued in co-operation with workers from other disciplines, from academia and industry.

In particular our team works on ( tasks in collaboration with team in bracket)

-adaptive numerics (task 15 , team G1);
- numerical methods for balance laws with rough coefficients (task 15 , teams D2 and A1);
- stability of nonlinear waves (task 12 , team D2);
- industrial project on computational electro-magnetics (task 13 , team F2);
- Hamilton-Jacobi equations (task 13 , teams E1 and E2);- degenerate parabolic equations (task 13 , team F2);
- front tracking (task 11 and 16 , teams I2 and I3);
- industrial project on multiphase flow (task 16 );
- numerics for stochastic differential equations (task 16 , team G1);
- nonlinear oceanic flows (task 14 ).

The research of the group at the department of Numerical Analysis, KTH, is closely integrated with the Parallel and Scientific Computing Institute, a Swedish national NUTEK center of excellence, and also with the Center for Parallel Computers. Parallel and Scientific Computing Institute (PSCI) is initiated by KTH, NUTEK and Swedish industry. The institute supplies competence and resources to Swedish industry in mathematical modeling, in numerical methods, and in computer science. The annual budget of PSCI is approximately 1.8 M EURO.

The Norwegian group has since their early work on front tracking methods close collaboration with the SINTEF applied mathematics institute, Numerical Objects (web: www.nobjects.com/ ; the developer of Diffpack) and industrial partners in particular in the petroleum industry.

Collaboration between the Swedish and Norwegian partners was started with a joint workshop in 1993 on hyperbolic differential equations. The special year at Mittag-Leffler Institute 1997-98 on Computational methods for differential equations had many participants from the present team. Current research interests between the Swedish and Norwegian team includes properties of hyperbolic equations and numerical methods for stochastic differential equations.

Members of the team and project involvement in percentage of full time employement:

- A. Szepessy (TO) (KTH Stockholm, 30%);  - B. Engquist (SAB) (KTH Stockholm, 20%);  - G. Kreiss (KTH Stockholm, 25%);  - H.O. Kreiss (KTH Stockholm, 20%);  - J. Oppelstrup (KTH Stockholm, 20%);  - B. Sjögreen (KTH Stockholm, 25%);  - H. Holden (TC) (NTNU Trondheim, 20%);  - P. Lindqvist (NTNU Trondheim, 20%);  - N.H. Risebro (U. Oslo, 20%);  - A. Tveito (U. Oslo, 10%);  - K.H. Karlsen (U. Bergen, 20%).


Two significant publications for the IHP project, from the KTH/Norway team, are:

[1] H. Holden, B. Oksendal, J. Uboe, T. Zhang; Stochastic Partial Differential Equations , Birkhauser, 1996.

[2] A. Szepessy, Lectures on stability of nonlinear waves in viscous media and numerics. Analysis of Systems of Conservation Laws , (Aachen, 1997), 199--261, Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., 99, Chapman & Hall/CRC, Boca Raton, FL, 1999. 

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