Research Article

Guaranteed computable bounds for the exact error in the finite element solution—Part II: bounds for the energy norm of the error in two dimensions†

  1. T. Strouboulis1,
  2. I. Babuška2,*,
  3. S. K. Gangaraj1

Article first published online: 9 FEB 2000

DOI: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<427::AID-NME779>3.0.CO;2-1

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Special Issue: Richard H. Gallagher Memorial Issue

Volume 47, Issue 1-3, pages 427–475, 10 - 30 January 2000

Additional Information

How to Cite

Strouboulis, T., Babuška, I. and Gangaraj, S. K. (2000), Guaranteed computable bounds for the exact error in the finite element solution—Part II: bounds for the energy norm of the error in two dimensions. Int. J. Numer. Meth. Engng., 47: 427–475. doi: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<427::AID-NME779>3.0.CO;2-1

Author Information

  1. 1

    Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, U.S.A.

  2. 2

    Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX 78712, U.S.A.

*TICAM, The University of Texas at Austin, TAY 2-400, Austin, TX 78712, U.S.A.

  1. †

    Dedicated to the memory of Dr. Richard H. Gallagher

Publication History

  1. Issue published online: 9 FEB 2000
  2. Article first published online: 9 FEB 2000
  3. Manuscript Received: 17 FEB 1999

Funded by

  • U.S. Army Research Office. Grant Number: DAAL03-G-028
  • National Science Foundation. Grant Number: MSS-9025110
  • U.S. Office of Naval Research. Grant Numbers: N00014-96-1-0021, N00014-96-1-1015
  • U.S. Office of Naval Research. Grant Number: N00014-90-J-1030
  • National Science Foundation. Grant Numbers: DMS-91-20877, DMS-95-01841

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Keywords:

  • a posteriori error estimation;
  • finite element method;
  • guaranteed error bounds;
  • upper and lower error bounds

Abstract

This paper addresses the computation of guaranteed upper and lower bounds for the energy norm of the exact error in the finite element solution. These bounds are constructed in terms of the solutions of local residual problems with equilibrated residual loads and are rather sharp, even for coarse meshes. he sharpness of the bounds can be further improved by employing few iterations of a relatively inexpensive iterative scheme. he main result is that the bounds are guaranteed for the nergy norm of the exact error, unlike the bounds which ave been proposed in [13,14] which are guaranteed only for the nergy norm of the error with respect to an enriched (truth-esh) finite element solution. Copyright © 2000 John Wiley & Sons, Ltd.

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