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Numerical Mathematics and Advanced Applications - ENUMATH 2013 pp 125–132Cite as

Mimetic Finite Difference Method for Shape Optimization Problems

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

Abstract

We test the performance of the Mimetic Finite Difference method applied to a wide class of shape optimization problems. Adaptive strategies based on heuristic error indicators are also considered to validate the effectiveness of the numerical scheme.

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References

  1. P.F. Antonietti, L. Beirão da Veiga, C. Lovadina, M. Verani, Hierarchical a posteriori error estimators for the mimetic discretization of elliptic problems. SIAM J. Numer. Anal. 51(1), 654–675 (2012)

    Article  Google Scholar 

  2. L. Beirão da Veiga, V. Gyrya, K. Lipnikov, G. Manzini, Mimetic finite difference method for the Stokes problem on polygonal meshes. J. Comput. Phys. 228(19), 7215–7232 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Brezzi, A. Buffa, K. Lipnikov, Mimetic finite differences for elliptic problems. M2AN Math. Model. Numer. Anal. 43(2), 277–295 (2009)

    Google Scholar 

  4. F. Brezzi, K. Lipnikov, M. Shashkov, Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal. 43(5), 1872–1896 (2005) (electronic)

    Google Scholar 

  5. M.C. Delfour, J.-P. Zolésio, Shapes and Geometries. Advances in Design and Control, vol. 22, 2nd edn. (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2011)

    Google Scholar 

  6. G. Doǧan, P. Morin, R.H. Nochetto, M. Verani, Discrete gradient flows for shape optimization and applications. Comput. Methods Appl. Mech. Eng. 196(37–40), 3898–3914 (2007)

    Google Scholar 

  7. P. Morin, R. Nochetto, M. Pauletti, M. Verani, Adaptive finite element method for shape optimization. ESAIM Control Optim. Calc. Var. 18(4), 1122–1149 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. O. Pironneau, On optimum profiles in Stokes flow. J. Fluid Mech. 59, 117–128 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  9. T. Tiihonen, Shape optimization and trial methods for free boundary problems. RAIRO Modél. Math. Anal. Numér. 31(7), 805–825 (1997)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. MOX-Dipartimento di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milano, Italy

    P. F. Antonietti, Nadia Bigoni & Marco Verani

Authors
  1. P. F. Antonietti
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  2. Nadia Bigoni
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  3. Marco Verani
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Corresponding author

Correspondence to Marco Verani .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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Antonietti, P.F., Bigoni, N., Verani, M. (2015). Mimetic Finite Difference Method for Shape Optimization Problems. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_12

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