Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation
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HPCES006.pdf
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223.99 KB
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Author(s)
Sauer-Budge, A.M.
Huerta, A.
Bonet, J.
Peraire, Jaime
Date Issued
January 2003
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
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.
Subjects
finite element
output bounds
a posteriori error estimation
Poisson equation
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