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Output bound approximations for partial differential equations; application to the incompressible navier-stokes equations

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Industrial and Environmental Applications of Direct and Large-Eddy Simulation

Part of the book series: Lecture Notes in Physics ((LNP,volume 529))

Abstract

We describe an a posteriori finite element procedure for the efficient computation of lower and upper estimators for functional outputs of semilinear elliptic partial differential equations. The general theory is presented, and earlier applications of the procedure to a variety of different problems—including the Poisson equation, the advection-diffusion equation, elasticity problems, the Helmholtz equation, the Burgers equation, and eigenvalue problems—are reviewed. The method is then extended to treat incompressible flow problems, and numerical results are presented for a problem of natural convection in a complex enclosure.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    L. Machiels & A. T. Patera

  2. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    J. Peraire

Authors
  1. L. Machiels
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  2. J. Peraire
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  3. A. T. Patera
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Editor information

Sedat Biringen Haluk Örs Akin Tezel Joel H. Ferziger

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© 1999 Springer-Verlag

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Machiels, L., Peraire, J., Patera, A.T. (1999). Output bound approximations for partial differential equations; application to the incompressible navier-stokes equations. In: Biringen, S., Örs, H., Tezel, A., Ferziger, J.H. (eds) Industrial and Environmental Applications of Direct and Large-Eddy Simulation. Lecture Notes in Physics, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106096

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  • DOI: https://doi.org/10.1007/BFb0106096

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66171-9

  • Online ISBN: 978-3-540-48706-7

  • eBook Packages: Springer Book Archive

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