Hyperbolic Balance Laws: modeling, analysis, and numerics (hybrid meeting)

This workshop brought together leading experts, as well as the most promising young researchers, working on nonlinear hyperbolic balance laws. The meeting focused on addressing new cutting-edge research in modeling, analysis, and numerics. Particular topics included ill-/well-posedness, randomness and multiscale modeling, flows in a moving domain, free boundary problems, games and control

Nonlinear Hyperbolic Problems: modeling, analysis, and numerics

The workshop gathered together leading international experts, as well as most promising young researchers, working on the modelling, the mathematical analysis, and the numerical methods for nonlinear hyperbolic partial differential equations (PDEs). The meeting focussed on addressing outstanding issues and identifying promising new directions in all three fields, i.e. modelling, analysis, and numerical discretization. Key questions settled around the lack of well-posedness theories for multidimensional systems of conservation laws and the use of hyperbolic modelling beyond the classical topic of gas dynamics. A focal point in numerics has been the discretization of random evolutions and uncertainty quantification. Equally important, new multi-scale methods and schemes for asymptotic regimes have been considered

Finite elements for scalar convection-dominated equations and incompressible flow problems - A never ending story?

The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important problems in these fields are discussed

Hyperbolic Conservation Laws

[no abstract available

Self-Adaptive Methods for PDE

[no abstract available

A finite volume scheme for nonlinear degenerate parabolic equations

We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a satisfying long-time behavior. Moreover, it remains valid and second-order accurate in space even in the degenerate case. After describing the numerical scheme, we present several numerical results which confirm the high-order accuracy in various regime degenerate and non degenerate cases and underline the efficiency to preserve the large-time asymptotic