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A class of finite element methods, the Discontinuous Galerkin
Methods (DGM), has been under rapid development recently and has
found its use very quickly in such diverse applications as
aeroacoustics, semi-conductor device simula tion, turbomachinery,
turbulent flows, materials processing, MHD and plasma simulations,
and image processing. While there has been a lot of interest from
mathematicians, physicists and engineers in DGM, only scattered
information is available and there has been no prior effort in
organizing and publishing the existing volume of knowledge on this
subject. In May 24-26, 1999 we organized in Newport (Rhode Island,
USA), the first international symposium on DGM with equal emphasis
on the theory, numerical implementation, and applications. Eighteen
invited speakers, lead ers in the field, and thirty-two
contributors presented various aspects and addressed open issues on
DGM. In this volume we include forty-nine papers presented in the
Symposium as well as a survey paper written by the organiz ers. All
papers were peer-reviewed. A summary of these papers is included in
the survey paper, which also provides a historical perspective of
the evolution of DGM and its relation to other numerical methods.
We hope this volume will become a major reference in this topic. It
is intended for students and researchers who work in theory and
application of numerical solution of convection dominated partial
differential equations. The papers were written with the assumption
that the reader has some knowledge of classical finite elements and
finite volume methods."
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