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The L.P.D.E.M., a mixed finite difference method for elliptic problems

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Summary

A “mixed” finite difference method is analyzed for solving certain elliptic problems. This method, called L.P.D.E.M. (Locally exact Partial Differential Equation Method) was initially proposed in the frame of hydrodynamic lubrication. Convergence is obtained. Relations between this scheme and homogenization theory are also discussed. For a one-dimensional elliptic equation with no zero-order term and in conservative form, this method is an exact one. Some numerical results will also be given.

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Authors and Affiliations

  1. Centre de math. U.R.A. 740 C.N.R.S., I.N.S.A. de LYON Bât 403, F-69621, Villeurbanne Cedex, France

    M. Jai & G. Bayada

  2. Mecanique des contacts U.R.A. 856 C.N.R.S., I.N.S.A de LYON Bât 113, F-69621, Villeurbanne Cedex, France

    G. Bayada

  3. L.A.N., Math. U.R.A. 740 C.N.R.S., Université LYON I, F-69622, Villeurbanne Cedex, France

    M. Chambat

Authors
  1. M. Jai
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  2. G. Bayada
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  3. M. Chambat
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Jai, M., Bayada, G. & Chambat, M. The L.P.D.E.M., a mixed finite difference method for elliptic problems. Numer. Math. 63, 195–211 (1992). https://doi.org/10.1007/BF01385856

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  • DOI: https://doi.org/10.1007/BF01385856

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