Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Computational Methods for Singularly Perturbed Systems Slimane Adjerid, Mohammed Ai a, and Joseph E. Flaherty
 

Summary: Computational Methods for Singularly Perturbed Systems
Slimane Adjerid, Mohammed Ai a, and Joseph E. Flaherty
Abstract. The di culty encountered when solving singularly perturbed dif-
ferential equations is that errors introduced in layers pollute the solution in
smooth regions. Since a priori control of the errors in layers is di cult, special
methods must be designed to reduce or eliminate polluting errors. Success-
ful methods add dissipation to a computational scheme to enlarge layers to
the mesh spacing. We focus on a method of using special quadrature rules
to con ne spurious pollution e ects, such as excess di usion and non-physical
oscillations, to layers. In particular, we indicate that Radau and Lobatto quad-
rature are useful for, respectively, convection-di usion and reaction-di usion
systems. With large errors con ned to small regions, an adaptive technique
can successfully improve accuracy. The quadrature approach is suitable for use
with adaptive methods that both adjust meshes and vary method orders. We
describe the key aspects of such an adaptive strategy and present several ap-
plications. We also demonstrate an equivalence between the quadrature-based
methods and a generalized Galerkin least-squares stabilization.
1. Introduction
Singularly perturbed di erential systems arise throughout science and engineer-
ing. They feature diversespatial and temporal scalesthat complicate traditional nu-

  

Source: Adjerid, Slimane - Department of Mathematics, Virginia Tech

 

Collections: Mathematics