Finite Element Bounds for Linear Functionals of Exact Solutions to the Three-Dimensional Poisson's Equation

S. Ghomeshi, Z. Cheng, and M. Paraschivoiu (Canada)


Poisson equation, output bounds, exact solution, three di mensional, FETI, certainty


A method for obtaining rigorous upper and lower bounds to an output of the exact solution of the three dimensional Poisson problem is described. More recently bounds to the exact outputs of interest have been obtained for both the Poisson equation and the advection-diffusion-reaction equation. In this work, the objective is to reduce the cost of these calculations in the context of three dimensional problems. The new ingredients are two-fold. First, the fi nite element tearing and interconnecting (FETI) procedure is invoked in order to calculate the inter-subdomain conti nuity multipliers (hybrid fluxes) and extend the approach to three space dimensions where bounds to the exact out put of interest in a cube geometry are reported. Second, the computational cost is reduced by using the FETI pro cedure because the primal and adjoint field solutions can be calculated jointly with the hybrid fluxes required for the subdomain problem.

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