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Error Bounds for L 1 Galerkin Approximations of Weakly Singular Integral Operators

In: Integral Methods in Science and Engineering, Volume 2

Author

Listed:
  • M. Ahues

    (Université de Lyon, Laboratoire de Mathématiques de l’Université de Saint-Étienne)

  • F. D. d’Almeida

    (Universidade do Porto)

  • R. Fernandes

    (Universidade do Minho)

Abstract

From all standard projection approximations of a bounded linear operator in a Banach space, a general (i.e., not necessarily orthogonal) Galerkin scheme ([At97] and [ALL01]) is the simplest one from a computational point of view. In this chapter, we give an upper bound of the relative error in terms of the mesh size of the underlying discretization grid on which no regularity assumptions are made. A weakly singular second kind Fredholm integral equation is used as an application to illustrate the actual sharpness of the error estimates. As is usual in the case of weakly singular error bounds, the sharpness of our bound is rather poor compared with practical results.

Suggested Citation

  • M. Ahues & F. D. d’Almeida & R. Fernandes, 2010. "Error Bounds for L 1 Galerkin Approximations of Weakly Singular Integral Operators," Springer Books, in: Christian Constanda & M.E. Pérez (ed.), Integral Methods in Science and Engineering, Volume 2, chapter 1, pages 1-10, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4897-8_1
    DOI: 10.1007/978-0-8176-4897-8_1
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