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On Computational Properties of a Posteriori Error Estimates Based upon the Method of Duality Error Majorants

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Maxim Frolov

    (University of Jyväskylä, Department of Mathematical Information Technology)

  • Pekka Neittaanmäki

    (University of Jyväskylä, Department of Mathematical Information Technology)

  • Sergey Repin

    (V.A. Steklov Institute of Mathematics in St.-Petersburg)

Abstract

Summary In the present paper, we analyze computational properties of the functional type a posteriori error estimates that have been derived for elliptic type boundary-value problems by duality theory in calculus of variations. We are concerned with the ability of this type of a posteriori estimates to provide accurate upper bounds of global errors and properly indicate the distribution of local ones. These questions were analyzed on a series of boundary-value problems for linear elliptic operators of 2nd and 4th order. The theoretical results are confirmed by numerical tests in which the duality error majorant for the classical diffusion problem is compared with the standard error indicator used in the MATLAB PDE Toolbox. Numerical tests performed show that the meshes generated on the basis of the majorant are very close to those that would be computed if on each step of the mesh refinement process we knew the exact error distribution. At the same time, meshes generated by the MATLAB code may considerably differ from them.

Suggested Citation

  • Maxim Frolov & Pekka Neittaanmäki & Sergey Repin, 2004. "On Computational Properties of a Posteriori Error Estimates Based upon the Method of Duality Error Majorants," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 346-357, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_32
    DOI: 10.1007/978-3-642-18775-9_32
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