Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation
Name
FDRL_TR-03-1.pdf
Size
223.99 KB
Format
Adobe PDF
Checksum (MD5)
f19814758f586666a58b31b1e6014aa4
Author(s)
Sauer-Budge, A. M.
Bonet, J.
Huerta, A.
Peraire, J.
Date Issued
2003
Publisher
Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology
Series/Report no.
ACDL Technical Reports;FDRL TR-03-1
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
Poisson Equation
A Posteriori Error Estimation
Output Bounds
Finite Element
Persistent DSpace Link
