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of the 13th Workshop on Numerical Methods for Problems with Layer Phenomena
(Moscow, 06-09 April 2016)

06.04.2016 (Wednesday)
16.30-18.00 ­ short welcome party (on the participant's desire), free discussions, tea, coffee ­
room 3-82 (3d floor) of the Building of Physics Faculty (see the scheme).

07.04.2016 (Thursday)
09:00-09:40 ­ 09:40-10:00 ­ registration opening of the Workshop

Registration and all sessions of the Workshop will be held in the room 2-38 (2nd floor) of the Second Humanities Building of MSU (see the scheme). Organizers provide laptop, data projector and whiteboard for the presentations.


07.04.2016 (Thursday)
Session 1
10:00-10:20 10:20-10:40 10:40-11:00 11:00-11:20 11:20-11:40 ­ ­ ­ ­ ­

(chairman ­ M. Stynes)
N. Kopteva V. Andreev H.-G. Roos S. Franz, H.-G. Roos A posteriori error estimates for singularly perturbed reactiondiffusion problems on anisotropic meshes. HЖlder estimates for a solution of a singularly perturbed convection-diffusion equation in a half-plane. Error estimation in balanced norms for second order problems. Robust error estimation for singularly perturbed fourth-order problems.

N. Nefedov, D. Lukyanenko, E. Nikulin, V. Volkov Asymptotic analysis of singularly perturbed periodic in time reaction-advection-diffusion problems and it's use for numerical methods.

11:40-12:00 ­

coffee-break (chairman ­ N. Nefedov)

Session 2
12:00-12:20

­ G. Shishkin

Computer difference schemes for singularly perturbed convectiondiffusion and reaction-diffusion equations in the presence of disturbances. Numerical solution of a singularly perturbed initial-boundary value problem with a Neumann condition for a parabolic equation.

12:20-12:40 12:40-13:00

­ L. Shishkina

­ S. Dobrokhotov, D. Minenkov, V. Nazaikinskii, B. Tirozzi Analytical-numerical algorithm for the run-up of long waves generated by localized sources on a curvilinear shore. ­ A. Zadorin ­ P. Vabishchevich Interpolation formulas for functions with large gradients in a boundary layer. A singularly perturbed boundary value problems with fractional powers of elliptic operators.

13:00-13:20 13:20-13:40

13:40-15:20
Session 3
15:20-15:40 15:40-16:00 16:00-16:20 16:20-16:40

­
(chairman ­ L. Recke)

lunch

­ V. Sobolev ­ E. Shchepakina ­ I. Kashchenko ­ M. Terentyev

Critical cases in control problems with singular perturbations. Geometric approach to the analysis of singularly perturbed models of biology and optics. Local dynamics of two-component contrast parabolic systems. Nonexistence and blow-up phenomena in singularly perturbed problems in the case of exchange of stabilities.

16:40-17:00 ­

coffee-break


Session 4
17:00-17:20 17:20-17:40

(chairman ­ V. Sobolev)
­ N. Levashova, A. Melnikova, S. Bytsura Internal layers in systems of parabolic equations. ­ M. Davydova, N. Nefedov The solutions with lnternal layers in multidimensional problems of the reaction-diffusion-advection type with balanced nonlinearity. ­ S. Aleshin, S. Glyzin, S. Kaschenko Spatially inhomogeneous solutions of KPP equation with delay. ­ D. Lukyanenko, V. Volkov, N. Nefedov Some new approaches of dynamic adaptive mesh construction for efficient numerical solving of singularly perturbed equations.

17:40-18:00 18:00-18:20

19:00

­

the Conference Dinner

(see the scheme)

______________________________________________________________________ 08.04.2016 (Friday)
Session 5
09:30-09:50 09:50-10:10 10:10-10:30 10:30-10:50 10:50-11:10

(chairman ­ G. Shishkin)
­ A.Hegarty, E. O'Riordan A singularly perturbed convection-diffusion problem posed on a circular domain. ­ M. Stynes ­ C. Xenophontos ­ S. Tikhovskaya Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation. The Reissner-Mindlin plate model and its numerical approximation. Solving an elliptic problem with regular boundary layers by multigrid method on Shishkin mesh.

­ A. Xiao, G. Zhang, X. Yi, J. Zhou Implicit-explicit multistep methods for stiff delay differential equations.

11:10-11:40 ­

coffee-break (chairman ­ H.-G. Roos)

Session 6
11:40-12:00 12:00-12:20 12:20-12:40

­ S. Becher ­ A. Belov, N. Kalitkin ­ I. Belukhina

FEM-analysis on graded meshes for turning point problems exhibiting an interior layer. Numerical solving of Cauchy problems with contrast structures. On mesh approximation accuracy of boundary-value problem for a singularly perturbed equation with one or two small parameters and non-smooth boundary functions. Uniform boundedness of Galerkin projection and the convergence of the grid adaptation algorithms for singular perturbed boundary value problems. On accuracy of the difference solutions of Dirchlet problem with a discontinuous derivative of the boundary function for singularly perturbed convection-diffusion equation.

12:40-13:00

­ I. Blatov, E. Kitaeva

13:00-13:20

­ T. Ershova


13:20-15:00
Session 7
15:00-15:20 15:20-15:40

­

lunch

(chairman ­ N. Kopteva)
­ A. Bykov Numerical scheme for the pseudoparabolic singularly perturbed ininialboundary problem with interior layer.

­ M. Dmitriev, B. Dobronets On the question of the individual optimal difference schemes for ordinary differential equations. ­ M. Ni, A. Wang ­ O. Omel'chenko ­ L. Recke The step-type contrast structure for a quasi-linear singular singularly perturbed boundary problem. Spike solutions to singularly perturbed elliptic problems. Boundary layer solutions to time-periodic singularly perturbed parabolic problems.

15:40-16:00 16:00-16:20 16:20-16:40 16:40-17:00

­ V. Butuzov, N. Nefedov, L. Recke, K. Schneider Asymptotics and stability of a periodic solution to a singularly perturbed parabolic problem in case of a double root of the degenerate equation.

17:00

­

Closing of the Workshop

__________________________________________________________________________________

Poster Session
(07-08 April, room 2-38)
V. Beloshapko S. Bytsura, N. Levashova A singularly perturbed elliptic problem with three-band boundary layer. The solution in the form of a moving front with the system of equations of FitzHugh-Nagumo type.

M. Davydova, N. Levashova, S. Zakharova The asymptotical analysis for the problem of modelling the gas admixture transport in the surface layer of the atmosphere. Zh. Dombrovskaya V. Golubenets A. Kashchenko A. Melnikova, R. Argun N. Nefedov, E. Nikulin FDTD method at the dielectric interfaces. Bifurcation analysis of logistic equation with state-dependent delay. Stability of automodel cycles in one equation derived from the laser model. Stationary solution with internal layer in one activator-inhibitor system. Existence and stability of periodic solutions to reaction-diffusion equations in the two-dimensional case.

__________________________________________________________________________________

09.04.2016 (Saturday) 09:30 ­ 14.00 ­
a trip to the park-museum "Kolomenskoye".
Transfer will be organized at 09:15-09:30 from the "Universitetskaya" hotel or from the Building of the Physics Faculty (details will be specified).