Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations.

摘要

In this project we have developed reduced basis approximations and associated a posteriori error bounds for parametrized partial differential equations. For this development to be of relevance to AFOSR applications, careful attention has to be paid to numerical analysis; computational procedures; performance assessment; and the application to non-trivial test cases. The approach is at present relevant to linear coercive and noncoercive and nonlinear elliptic equations, linear coercive and weakly noncoercive and nonlinear parabolic equations, and certain classes of linear hyperbolic equations. Applications considered include heat transfer, acoustics, elasticity, fluid dynamics, and electromagnetics.