Parameter-Robust Numerical Methods for
Singularly Perturbed and Convection-Dominated
Problems
Organizers
Owe Axelsson
Faculty of Mathemtics and Informatics,
Catholic University of Nijmegen,
Nijmegen, The Netherlands
axelsson@sci.kun.nl
Pieter W. Hemker
CWI, Amsterdam, The Netherlands
P.W.Hemker@cwi.nl
and
Grigorii I. Shishkin
Institute of Mathematics and Mechanics, Ural Branch of Russian
Academy of Sciences, Ekaterinburg, Russia
Grigorii@shishkin.ural.ru
Abstract
Numerical modeling of processes and phenomena in many fields of
science and engineering leads one to boundary value problems for
PDEs, the solution of which have singularities. This class includes, in
particular, singularly perturbed equations, i.e., equations with a
small parameter multiplying the highest derivatives. Among these
are the Navier-Stokes equations of fluid flow at high Reynolds number,
the drift-diffusion equations of semiconductor device simulation,
mathematical models of the spreading of pollutants or in chemical
kinetics. The solutions of these problems contain thin boundary and
interior layers. The singular behaviour of the solution in a thin layer
generally gives rise to difficulties in the numerical solution by
traditional
methods. The problem of resolving layers, which is of great practical
importance, is still not solved satisfactorily for a wide class of
singular perturbation problems. The minisymposium will concern a
variety of techniques in the field of parameter-robust and efficient
numerical methods for such problems, including adaptive grid-refinement
procedures, decomposition and defect correction techniques, the
additive
splitting of singularities, and so on. This field has witnessed a
stormy
development in the last years. The main goal of the minisymposium is
to consolidate efforts of the investigators in further research of
parameter-robust methods.
Presentations
-
P. W. Hemker, G.I. Shishkin and L.P. Shishkina,
The Numerical Solution of a Neumann Problem
for Parabolic Singular Perturbed Equations
with High-Order Time Accuracy
-
G.I. Shishkin,
Grid approximations of singularly perturbed elliptic equations with
convective terms in unbounded domains
-
O. Axelsson,
The standard Galerkin and the streamline upwind finite element methods
for a priori chosen meshes; uniform in $\varepsilon$ convergence in
$L_2$-norm
-
M. Nikolova and O. Axelsson,
Adaptive Refinement Procedure for Singularly Perturbed
Convection-Diffusion Problems
-
L. Tobiska,
Convergence of a streamline-diffusion method
for nonconforming finite element approximations
applied to the incompressible Navier-Stokes equation
-
I. Boglaev,
Finite Difference Domain Decomposition for a Singularly Perturbed
Parabolic Problem
-
I.V. Tselishcheva and G.I. Shishkin,
A decomposition method for singularly perturbed
reaction-diffusion equations
-
D. Funaro,
Operator Dependent Grids
-
P. W. Hemker, G.I. Shishkin and L.P. Shishkina,
An $\varepsilon$-uniform deffect-correction method
for a parabolic convection-diffusion problem
- K. Al-Khaled,
Since Approximation of Solution of Burgers' Equation with
Discontinuous Initial Condition