US-France Cooperative Research: Numerical Simulation by Spectral Element Method

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This award will support collaborative research in computational fluid dynamics and numerical analysis between Dr. Anthony Patera, Massachusetts Institute of Technology and Dr. Yvon Maday, Laboratory for Numerical Analysis, University of Pierre and Marie Curie, Paris, France. The objective of the proposed project is a rigorous analysis of certain aspects of spectral methods as applied to equations governing fluid flow. The numerical simulation of phenomena governed by partial differential equations is currently of major interest. This has become even more true as computers have become more powerful and able to solve problems that used to be intractable on previous machines. In order to be able to provide a numerical solution with sufficient accuracy, the numerical methods have to become more precise and the standard methods often fail to give a satisfactory accuracy. The research of new high order methods is thus of fundamental importance. Spectral methods are amongst the most accurate numerical methods currently available for the numerical simulation of physical phenomena. In this project, the investigators propose to continue the development of the Spectral Element method, along with a rigorous mathematical theory. The project will benefit from the complementary expertise of the two investigators. Professor Maday is a leading mathematician and has made many contributions to the rigorous development of spectral and finite element methods. The Spectral Element Method was introduced by Patera and is an important contribution to the development of spectral methods.