## EVENT DETAILS AND ABSTRACT

**Number Crunch Lunch Seminar**
**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).

**Date:** Thursday, June 01, 2000

**Time:** 4:00pm

**Where:** Tech MG28

**Contact Person:** David Chopp & Mike Miksis

**Contact email:** chopp@nwu.edu,miksis@nwu.edu

**Contact Phone:** 847-491-8391,847-491-5585

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