Construction of Accurate, Robust and Efficient Numerical Techniques for Partial Differential Equations

点击翻译按钮获取中文摘要

9973328The main objectives of this research are the construction and study of finite element approximations to steady-state and transient problems of mechanics and engineering, including convection-diffusion-reaction problems, Stokes and Navier-Stokes equations, equations of linear elasticity, and the construction, analysis, and testing of fast methods for solving the resulting discrete systems. The emphasis will be on the development of new accurate, robust and efficient computational techniques. Approximation strategies involving standard Galerkin finite element methods, least-squares methods, and mixed finite element methods will be studied especially from the standpoint of their accuracy, stability, and efficient implementation. The solution techniques which will be developed will emphasize preconditioning via domain decomposition or multigrid/multilevel methods. Local grid refinement and error control coupled with multilevel solution methods will be used in ground water and petroleum applications.Technological development is becoming increasingly dependent on large scale scientific computation. Such computations are often limited by accuracy of the numerical method and the amount of computational effort required for its solution. The research funded by this proposal will provide better numerical methods and new techniques for the efficient solution of the resulting system of linear and non-linear equations. Such advances will improve our ability to accurately model more complex processes (devices) as well as our ability to understand complex systems such as the behavior of a contaminant in a multi-component groundwater system.