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This volume is the Proceedings of the Workshop on Analytical and
Computational Methods for Convection-Dominated and Singularly
Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31
August 1998. The workshop attracted about 50 participants from 12
countries. The volume includes 13 invited lectures and 19
contributed papers presented at the workshop and thus gives an
overview of the latest developments in both the theory and
applications of advanced numerical methods to problems having
boundary and interior layers. There was an emphasis on experiences
from the numerical analysis of such problems and on theoretical
developments. The aim of the workshop was to provide an opportunity
for scientists from the East and the West, who develop robust
methods for singularly perturbed and related problems and also who
apply these methods to real-life problems, to discuss recent
achievements in this area and to exchange ideas with a view of
possible research co-operation.
Since the first edition of this book, the literature on fitted mesh
methods for singularly perturbed problems has expanded
significantly. Over the intervening years, fitted meshes have been
shown to be effective for an extensive set of singularly perturbed
partial differential equations. In the revised version of this
book, the reader will find an introduction to the basic theory
associated with fitted numerical methods for singularly perturbed
differential equations. Fitted mesh methods focus on the
appropriate distribution of the mesh points for singularly
perturbed problems. The global errors in the numerical
approximations are measured in the pointwise maximum norm. The
fitted mesh algorithm is particularly simple to implement in
practice, but the theory of why these numerical methods work is far
from simple. This book can be used as an introductory text to the
theory underpinning fitted mesh methods.
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