TY - JOUR
T1 - Petrov-Galerkin Method with Local Green's Functions in Singularly Perturbed Convection-Diffusion Problems
AU - O. Axelsson, E. Glushkov & N. Glushkova
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 127
EP - 146
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/925.html
KW - convection-diffusion equation, Petrov-Galerkin discretization, Fourier transform, integral equations, iterative solution.
AB - <p style="text-align: justify;">Previous theoretical and computational investigations have
shown high efficiency of the local Green&#39;s function method for the
numerical solution of singularly perturbed problems with sharp boundary
layers. However, in several space variables those functions, used as
projectors in the Petrov-Galerkin scheme, cannot be derived in a closed
analytical form. This is an obstacle for the application of the method
when applied to multi-dimensional problems. The present work proposes a
semi-analytical approach to calculate the local Green&#39;s function, which
opens a way to effective practical application of the method. Besides
very accurate approximation, the matrix stencils obtained with these
functions allow the use of fast and stable iterative solution of the
large sparse algebraic systems that arise from the grid-discretization.
The advantages of the method are illustrated by numerical examples.</p>