This volume covers the proceedings ofthe ICASE/LaRC workshop on "Finite Element Theory and Application" held during July 28-30, 1986. The purpose of this workshop was to provide an update on the status of finite element theory, to assess the impactoftbis theory on practice, and to suggest directions for Cuture research. There were thirteen participants in the workshop. Some of them were leading mathematicians working on the finite element theory, and the rest expert practitioners in the areas of fluid dynamics and structural analysis. The first six articles in this volume provide a brief review of the theoretical and computational aspects of finite element methods (FEM). The remaining seven articles deal with a variety of applications highlighting the type of results that are possible, and indicating areas which deserve future research. The first article is by Temam. lt provides an introduction and overview of the general finite element methods for the nonspecialist. lt also illustrates the power of finite element methods with two specific applications-the free surface flowjstructure interaction problern and the compressible Euler solu tion to the flow past a finite aspect ratio flat plate at incidence. The second article by Brezzi is againan introduction and overview ofmixed finite element methods. lt includes a brief discussion of special techniques for solving the discrete problem, as weil as some applications to certain basic problems in elasticity and hydrodynamics."

The Institute for Computer Applications in Science and Engineer ing (ICASE) and NASA Langley Research Center (LaRC) brought together on October 2-4, 1989 experts in the various areas of com bustion with a view to expose them to some combustion problems of technological interest to LaRC and possibly foster interaction with the academic community in these research areas. The top ics chosen for this purpose were flame structure, flame stability, flame holding/extinction, chemical kinetics, turbulence-kinetics in teraction, transition to detonation, and reacting free shear layers. The lead paper set the stage by discussing the status and issues of supersonic combustion relevant to scramjet engine. Then the ex perts were called upon i) to review the current status of knowledge in the aforementioned ;:I. reas, ii) to focus on how this knowledge can be extended and applied to high-speed combustion, and iii) to suggest future directions of research in these areas. Each topic was then dealt with in a position paper followed by formal discussion papers and a general discussion involving the participants. The position papers discussed the state-of-the-art with an emphasis on key issues that needed to be resolved in the near future. The discussion papers crit ically examined these issues and filled in any lacunae therein. The edited versions of the general discussions in the form of questions from the audience and answers from the speakers are included wher ever possible to give the reader the flavor of the lively interactions that took place.

Turbulence is the lIDst natural nDde of fluid lIDtion, and has been the subject of scientific study for all Dst a century. During this period, various ideas and techniques have evolved to nDdel turbulence. Following Saffman, these theoretical approaches can be broadly divided into four overlapping categories -- (1) analytical lIDdelling, (2) physical lIDdelling, (3) phenomenologicalllDdelling, and (4) nurerical lIDdelling. With the purpose of stmtnarizing our =ent understanding of these theoretical approaches to turbulence, recognized leaders (fluid dynamicists, mathematicians and physicists) in the field were invited to participate in a formal workshop during October 10-12, 1984, sponsored by The Institute for CooIputer Applications in Science and Engineering and NASA Langley Research Center. Kraiciman, McCcxnb, Pouquet and Spiegel represented the category of analytical nDdelling, while Landahl and Saffman represented physical lIDdelling. The contributions of Latmder and Spalding were in the category of phenanenological lIDdelling, and those of Ferziger and Reynolds in the area of nurericalllDdelling. Aref, Cholet, Lumley, Moin, Pope and Temam served on the panel discussions. With the care and cooperation of the participants, the workshop achieved its purpose, and we believe that its proceedings published in this vol\. llre has lasting scientific value. The tone of the workshop was set by two introductory talks by Bushnell and ChaImm. Buslmell presented the engineering viewpoint while Chapman reviewed from a historical perspective developments in the study of turbulence. The remaining talks dealt with specific aspects of the theoretical approaches to fluid turbulence.