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Superconsistent Discretizations

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Abstract

We say that the approximation of a linear operator is superconsistent when the exact and the discrete operators coincide on a functional space whose dimension is bigger than the number of degrees of freedom needed in the construction of the discretization. By providing several examples, we show how to build up superconsistent schemes. Many open questions will be also rised and partially discussed.

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REFERENCES

  1. Christie, I., Griffiths, D. F., Mitchell, A. R., and Zienkiewicz, O. C. (1976). Finite element method for second order differential equations with significant first derivatives. Internat. J. Numer. Methods Engrg. 10, 1389–1396.

    Google Scholar 

  2. Deville, M. O., and Mund, E. H. (1992). Finite element preconditioning of collocation schemes for advection-diffusion equations. In Beauwens, R., and de Groen, P. (eds.), Iterative Methods in Linear Algebra, North Holland.

  3. Elliot, D. (1982). The classical collocation method for singular integral equations. SIAM J. Numer. Anal. 19(4), 816–832.

    Google Scholar 

  4. Funaro, D. (1997). Some remarks about the collocation method on a modified Legendre grid. Comput. Math. Appl. 33(1/2), 95–103.

    Google Scholar 

  5. Funaro, D. (1997). Spectral Elements for Transport-Dominated Equations, LNCSE, No. 1, Springer, Heidelberg.

    Google Scholar 

  6. Funaro, D. (1999). A note on second-order finite-differences schemes on uniform meshes for advection-diffusion equations. Numer. Methods PDEs 15, 581–588.

    Google Scholar 

  7. Funaro, D. (2000). About 3-D spectral elements computations. In Trigiante, D. (ed.), Recent Trends in Numerical Analysis, NOVA Science Publishers.

  8. Funaro, D. (2001). A superconsistent Chebyshev collocation method for second-order differential operators. Numerical Algorithms.

  9. Funaro, D. Superconsistent discretizations of integral type equations. to appear.

  10. Hughes, T. J. R. (1978). A simple scheme for developing “upwind” finite elements, Internat. J. Numer. Methods Engrg. 12, 1359–1365.

    Google Scholar 

  11. Srivastav, R. P. (1983). Numerical solution of singular integral equations using Gauss type formulae, I: Quadrature and collocation on Chebyshev nodes. IMA J. Numer. Anal. 3, 305–318.

    Google Scholar 

  12. Tricomi, F. G. (1957). Integral Equations, Interscience Publishers, New York.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Modena, Modena, Italy

    Daniele Funaro

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  1. Daniele Funaro
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Funaro, D. Superconsistent Discretizations. Journal of Scientific Computing 17, 67–79 (2002). https://doi.org/10.1023/A:1015136227726

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  • DOI: https://doi.org/10.1023/A:1015136227726

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