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Numerical evaluation of FEM with application to the 1D advection-diffusion problem

  • G. Sangalli
Conference paper

Summary

We present a numerical procedure to evaluate the efficiency of finite element numerical methods. We improve some of the ideas proposed in previous works, and we give a theoretical and empirical justification in a general framework. The proposed procedure performs an eigenvalue computation, and requires the knowledge of the behavior of the exact operator in order to choose proper norms for the evaluations. In the experiments we focus our attention on the 1D advection-diffusion problem: we show that our numerical procedure gives actually very sharp indications about the optimality of the tested numerical methods.

Keywords

Saddle Point Problem Empirical Justification Eigenvalue Computation Standard Finite Element Method Sharp Indication 
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References

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    Babuška, I., Aziz, A.K. (1972): Survey lectures on the mathematical foundations of the finite element method. In: Aziz, A.K. (ed.): The mathematical foundations of the finite element method with applications to partial differential equations. Academic Press, New York, pp. 1–359Google Scholar
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    Sangalli, G. (2002): Numerical evaluation of FEM with application to the 1D advection-diffusion problem. Math. Models Methods Appl. Sci. 12, 205–228MathSciNetMATHCrossRefGoogle Scholar
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    Xu, J., Zikatanov, L. (2002): Some observations on Babuška and Brezzi theories. Numer. Math., to appear; DOI 10.1007/s002110100308Google Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • G. Sangalli
    • 1
  1. 1.Dipartimento di Matematica “F. Casorati”Università di PaviaPaviaItaly

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