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International Conference: BAIL 2006 Boundary and Interior Layers - Computational & Asymptotic Methods - |
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Minisymposia |
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Call for Minisymposium Proposals The Organizing Commitee welcomes Proposals for minisymposia. The proposed title of the minisymposium, a list of speakers and a short abstract appropriate for public posting should be submitted. A minisymposium consists of four to six talks with a common technical theme. Minisymposium organizers are responsible for participation of their speakers and collecting and forwarding initial speaker and talk title information. Minisymposia are allowed two and a half hours each. Please submit the proposals by e-mail to Prof. Dr. Gert Lube at lube@math.uni-goettingen.de. The partipication of young researchers is encouraged. Minisymposia proposals will be reviewed on a continuous basis until the proposal deadline, 16 December 2005. Accepted Minisymposia N. Kopteva, M. Stynes, E. O'Riordan: Robust methods for nonlinear singularly perturbed differential equations ABSTRACT: This mini-symposium is concerned with nonlinear singularly perturbed differential equations such as semilinear reaction-diffusion problems, quasilinear parabolic convection-diffusion equations, flows in porous media, and the modelling of catalytic chemical reactions and of turbulence. The talks deal with methods that are "robust" for such problems, i.e., that yield accurate approximations of the solution for a broad range of values of the singular perturbation parameter. This includes numerical methods for which numerical experiments demonstrate robustness for a wide range of values of the parameter, even though no theoretical proof of convergence exists. SPEAKER:
P. Houston, R. Hartmann Self-adaptive Methods for PDEs ABSTRACT: Many processes in science and engineering are formulated in terms of partial differential equations. Typically, for problems of practical interest, the underlying analytical solution exhibits localised phenomena such as boundary and interior layers and corner and edge singularities, for example, and their numerical approximation presents a challenging computational task. Indeed, in order to resolve such localised features, in an accurate and efficient manner, it is essential to exploit so-called self-adaptive methods.
Such approaches are typically based on a posteriori error estimates for the
underlying discretization method in terms of local quantities, such as local
residuals, computed from the discrete solution. Over the last few years, there
have been significant developments within this field in terms of both rigorous
a posteriori error analysis, as well as the subsequent design of optimal meshes.
In this minisymposium, a number of recent developments, such as the design of
high-order and hp-adaptive finite element methods will be considered, as
well as anisotropic mesh adaptation and mesh movement.
Debopam Das, Tapan Sengupta: Asymptotic Methods for Laminar and Turbulent boundary Layers ABSTRACT: The mini symposium will have contributions dealing with laminar/turbulent flows- their morphology and structures. Specifically, results would be presented that discuss the very concept of turbulent boundary layers. Also, detailed flow structures arising in mixed convection problem involving velocity and thermal boundary/ interior layers will be a focus of another contribution. This session will also have contributions dealing specifically with temporal and/or spatio-temporal growth of waves in boundary/ interior layers. For example, existence of spatio-temporal growth of waves in boundary layer is established for the first time that is related non-orthogonal modes proposed earlier for Couette and channel flows. The focus will be on receptivity and stability of equilibrium steady flows as well as unsteady bi-directional pipe flows that identifies non-axisymmetric modes. SPEAKER:
G.I. Shiskin, P. Hemker: Robust Methods for Problems with Layer Phenomena and Additional Singularities ABSTRACT: The minisymposium will be concerned with singularly perturbed multiscale problems having additional singularities. A complicated geometry or unbounedness of the domain and/or the lack of sufficient smoothness (or compatibility) of the problem data may result in singular solutions that have their own specific scales, besides boundary/interior layers. We intend to examine techniques for constructing numerical methods that converge parameter-uniformly (in the maximum norm).
The following research aspects will be also considered:
(i) As a rule, such parameter-uniformly convergent numerical methods have
too low order of uniform convergence, which restricts their applicability
in practice. With this respect, methods how to increase the accuracy of
parameter-uniformly convergent numerical methods will be considered.
(ii) When standard numerical methods, for example, domain decomposition
methods are used to find solutions of parameter-uniformly convergent
discrete approximations, the decomposition errors of the discrete
solutions and the number of iterations required to solve the discrete
problem depend on the perturbation parameter and grow when it tends to zero.
We will consider decomposition methods preserving the property of
parameter-uniform convergence. Domain decomposition and local defect correction
techniques allows us to reduce the construction of robust numerical methods
for multiscale problems to locally robust methods for monoscale problems
on the specific subdomains.
Other aspects and applications will be also under consideration.
Problems for partial differential equations with different types of
boundary and interior layers will be considered. To construct special
numerical methods, fitted meshes, which are a priori and
a posteriori condensing in the layer regions, are used.
J. Maubach, I, Tselishcheva: Robust Numerical Methods for Problems with Layer Phenomena and Applications ABSTRACT: 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. SPEAKER
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