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A Contact Problem for a Convection-diffusion Equation

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Integral Methods in Science and Engineering

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20.6 Conclusions

We have proposed an efficient iterative domain decomposition method that solves general convection-diffusion singular perturbation problems. Our specific application involves a piecewise constant diffusion coefficient. We have established sufficient conditions for the convergence of the method, identified suitable values of the relaxation parameter ϑ, and started investigations into the rate of convergence. The method was implemented to O(ε2) to solve test problems.

Full details of the proofs of these assertions will appear in a future publication.

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References

  1. C. Carlenzoli and A. Quarteroni, Adaptive domain decomposition methods for advection-diffusion problems, in Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, IMA Vol. Math. Appl. 75, Springer-Verlag, New York, 1995, 165–186.

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  2. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations, Clarendon Press, Oxford, 1999.

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  3. I. Chudinovich and C. Constanda, Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation, Chapman & Hall/CRC, Boca Raton-London-New York-Washington, DC, 2000.

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  4. C. Constanda, Solution Techniques for Elementary Partial Differential Equations, Chapman & Hall/CRC, Boca Raton-London-New York-Washington, DC, 2002.

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Author information

Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, University of Tulsa, 600 S. College Avenue, Tulsa, OK, 74104-3189, USA

    Shirley Pomeranz & Christian Constanda

  2. Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931-1295, USA

    Gilbert Lewis

Authors
  1. Shirley Pomeranz
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  2. Gilbert Lewis
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  3. Christian Constanda
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Editor information

Editors and Affiliations

  1. Department of Mathematical and Computer Sciences, University of Tulsa, 600 South College Avenue, Tulsa, OK, 74104, USA

    C. Constanda

  2. Department of Mathematics, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL, 32816, USA

    Z. Nashed  & D. Rollins  & 

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© 2006 Birkhäuser Boston

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Pomeranz, S., Lewis, G., Constanda, C. (2006). A Contact Problem for a Convection-diffusion Equation. In: Constanda, C., Nashed, Z., Rollins, D. (eds) Integral Methods in Science and Engineering. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4450-4_20

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