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IMA Journal of Numerical Analysis 1997 17(4):547-561; doi:10.1093/imanum/17.4.547
© 1997 by Institute of Mathematics and its Applications
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Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

M. AINSWORTH{dagger}, D. W. KELLY{ddagger}, I. H. SLOAN* and S. L. WANG**

Mathematics Department, Leicester University Leicester LE1 7RH, UK
School of Mechanical and Manufacturing Engineering, University of New South Wales Sydney 2052, Australia
School of Mathematics, University of New South Wales Sydney 2052, Australia
School of Mathematics and Statistics, Curtin University of Technology GPO Box U1987, Perth 6001, Australia

{dagger} Email: ain{at}mcs.le.ac.uk

{ddagger} Email: D.Kelly{at}unsw.edu.au

* Email: I.Sloan{at}unsw.edu.au

** Email: swang{at}cs.curtin.edu.au

It is shown how the finite element approximation of a nonlinear heat conduction problem may be post-processed to yield enhanced approximations to the solution and the flux at any point in the domain. Sharp computable bounds on the accuracy of the post-processed approximations are derived. A criterion is identified for guiding adaptive refinements of the finite element discretization. A numerical example is given illustrating the theoretical results.


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