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Second Conference on Numerical Analysis and Applications
June 11-15, 2000
University of Rousse
Rousse, Bulgaria |
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Organizers
Plamen Yalamov, Marcin Paprzycki, Lubin Vulkov
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High Order Splitting Time and Finite Difference Methods for 2D Parabolic Convection-Diffusion Problems
by
Carmelo Clavero
Departamento de Matemática Aplicada. Universidad de Zaragoza
Coauthors: B. Bujanda (Universidad de La Rioja), J.L. Gracia (Universidad de Zaragoza), J.C. Jorge (Universidad Pública de Navarra)
High Order Splitting Time and Finite Difference Methods
for 2D Parabolic Convection-Diffusion Problems
High Order Splitting Time and Finite Difference Methods
for 2D Parabolic Convection-Diffusion Problems
B. Bujanda 1, C. Clavero 2, J.L. Gracia 3,
J.C. Jorge 4
1 Departamento de Matemáticas y Computación,
Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa
s/n, 26004 Logroño, Spain. email:bbujanda@dmc.unirioja.es
2 Departamento de Matemática Aplicada. Universidad de
Zaragoza. Spain. e-mail: clavero@posta.unizar.es
3 Departamento de Matemática Aplicada. Universidad de
Zaragoza. Spain. e-mail: jlgracia@posta.unizar.es
4 Departamento de Matemática e Informática,
Universidad Pública de Navarra, Edificio Los Acebos, Campus
Arrosadía s/n, 31006 Pamplona, Spain.
email: jcjorge@unavarra.es
Abstract
In this work we consider a bidimensional time-dependent
convection-diffusion problem of type
|
ut -\epsilon\Deltau(x)+ v·Ñu+b u=f |
| (1) |
joined to suitable initial and boundary conditions, where
\epsilon can be small. In order to construct high order
robust methods to approach u, firstly, we reduce (1), by
using a high order splitting method, to a family of
one-dimensional singularly perturbed convection-diffusion
problems. After that, we discretize these problems with finite
difference methods (also of high order) which are uniformly
convergent with respect to parameter \epsilon, on some
special meshes. The totally discrete schemes obtained with this
technique, are optimal in terms of computational complexity, since
the number of arithmetic computations that they require depends
linearly on the number of mesh points.
Keywords: Uniform convergence,
splitting methods, high order, Shishkin mesh.
AMS Subject classification:
65N12, 65N30, 65N06.
Date received: February 10, 2000
Copyright © 2000 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caen-20.