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A Spectral Mortar Element Discretization of the Poisson Equation with Mixed Boundary Conditions

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In this paper, we study a spectral mortar element discretization of the Poisson equation on a square subject to mixed boundary conditions of Dirichlet and Neumann type. We carry out the numerical analysis of the method and derive error estimates. An efficient algorithm for the solution of the problem is proposed and numerical tests confirming the theoretical results are presented.

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References

  1. Azaïez, M., Bernardi, C., and Maday, Y. (1996). Some tools for adaptivity in the spectral element method (Proc. of the Third Int. Conf. On Spectral and High Order Methods, Houston J. of Math., 1996), pp. 243–253.

  2. Ben Belgacem F. (1999). The mortar finite element method with Lagrange multipliers. Numer. Math. 84, 173–197

    Article  MATH  MathSciNet  Google Scholar 

  3. Bernardi C., Maday Y. (2001). Spectral element discretizations of the Laplace equation with mixed boundary conditions. Appl. Math. Informatics 6, 1–29

    MATH  MathSciNet  Google Scholar 

  4. Bernardi, C., and Maday, Y. (1997). Spectral methods. In Ciarlet, P. G., and Lions, J.-L. (eds.), Handbook of Numerical Analysis, Vol. V, North-Holland, pp. 209–485.

  5. Bernardi, C., Maday, Y., and Patera, A. T. (1990). A New Non Conforming Approach to Domain Decomposition: The Mortar Element Method, Collège de France Seminar, Pitman, H. Brezis & J.-L. Lions eds, 1990.

  6. Ciarlet, P. G. (1991). Basic error estimates for elliptic problems. In Ciarlet, P. G., and Lions, J.-L. (eds.), Handbook of Numerical Analysis, Vol. II, North-Holland, pp. 17–351.

  7. Grisvard P. (1985). Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24, Pitman, London

    MATH  Google Scholar 

  8. Lions J.-L., Magenes E. (1968). Problèmes aux Limites Non Homogènes. Dunod, Paris

    MATH  Google Scholar 

  9. Maday Y. (1989). Relèvement de traces polynômiales et interpolation Hilbertienne entre espaces de polynômes. C.R. Acad. Sci. Paris 309, (Série I), 463–468

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LMAM, UMR 7122, Université de Metz, Ile de Saulcy, 57045, Metz Cedex 01, France

    Zakaria Belhachmi

  2. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus

    Andreas Karageorghis

Authors
  1. Zakaria Belhachmi
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  2. Andreas Karageorghis
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Correspondence to Andreas Karageorghis.

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Belhachmi, Z., Karageorghis, A. A Spectral Mortar Element Discretization of the Poisson Equation with Mixed Boundary Conditions. J Sci Comput 30, 275–299 (2007). https://doi.org/10.1007/s10915-006-9095-7

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  • DOI: https://doi.org/10.1007/s10915-006-9095-7

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