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Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation

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Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation

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Author: Sauer-Budge, A. M.; Bonet, J.; Huerta, A.; Peraire, J.
Publisher: Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology
Date Issued: 2003
Abstract:
We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization.
URI: http://hdl.handle.net/1721.1/57596
Series/Report no.: ACDL Technical Reports;FDRL TR-03-1
Keywords: Poisson Equation, A Posteriori Error Estimation, Output Bounds, Finite Element

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