EVENT DETAILS AND ABSTRACT

Title: Output Bounds for Elliptic Partial Differential Equations: A General Formulation
Speaker: Professor Anthony T. Patera
Speaker Info: MIT
Brief Description:
Special Note: Note special time and place of the meeting
Abstract:

In the numerical solution of partial differential equations, the quantities of primary importance are not the full field variables, but rather the "outputs" --- such as forces and displacements, or transport rates or flowrates, or lifts and drags --- which represent the relevant engineering performance metrics. We describe here a general a posteriori output bound formulation for the efficient computation of sharp, rigorous, constant--free lower and upper bounds --- and hence error estimates --- for outputs which are functionals of the solutions of elliptic partial differential equations. The general formulation admits three rather different instantiations, each associated with different approximation schemes, and each corresponding to different computational relaxations (expanded spaces, "preconditioners," and generalized residuals): an adaptive finite--element discretization technique; a conjugate--gradient iteration stopping criterion; and a blackbox reduced--basis approximation approach. Applications include linear coercive symmetric equations (e.g., Poisson, elasticity), linear coercive nonsymmetric equations (e.g., convection--diffusion), linear noncoercive equations (e.g., Helmholtz), and nonlinear noncoercive equations (e.g., eigenvalue problems, incompressible Navier--Stokes).