Output bound approximations for partial differential equations; application to the incompressible navier-stokes equations

We describe an a posteriori finite element procedure for the efficient computation of lower and upper estimators for functional outputs of semilinear elliptic partial differential equations. The general theory is presented, and earlier applications of the procedure to a variety of different problems—including the Poisson equation, the advection-diffusion equation, elasticity problems, the Helmholtz equation, the Burgers equation, and eigenvalue problems—are reviewed. The method is then extended to treat incompressible flow problems, and numerical results are presented for a problem of natural convection in a complex enclosure.

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