J. Maubach, I, Tselishcheva

Robust Numerical Methods for Problems with Layer Phenomena and Applications

Numerical modeling of many processes and physical phenomena leads to boundary value problems for PDEs having non-smooth solutions with singularities of thin layer type. Among them are convection-dominated convection-diffusion problems, Navier-Stokes equations and boundary-layer equations at high Reynolds number, the drift-diffusion equations of semiconductor device simulation, flow problems with lift, drag, transition and interface phenomena, phenomena in plasma fluid dynamics, mathematical models for the spreading of pollutants, combustion, shock hydrodynamics or transport in porous media and other related problems. The solutions of these problems contain thin boundary and interior layers, shocks, discontinuities, shear layers, or current sheets, etc. The singular behaviour of the solution in such local structures generally gives rise to difficulties in the numerical solution of the problem in question by traditional methods on uniform meshes and requires the use of highly accurate discretization methods and adaptive grid refinement techniques. The problem of resolving layers, which is of great practical importance, is still not solved satisfactorily for a wide class of problems with layer phenomena and applications, which the minisymposium is concerned with.