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The discrete maximum principle for stabilized finite element methods

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • E. Burman

    (DMA, Ecole Polytechnique Federale de Lausanne)

  • A. Ern

    (Ecole Nationale des Ponts et Chaussées (ENPC), CERMICS)

Abstract

Summary We investigate stabilized Galerkin approximations of certain steady and unsteady convection-diffusion problems with linear and nonlinear source terms. We derive nonlinear stream line and cross wind diffusion methods that guarantee a discrete maximum principle. Our theoretical results apply to finite element methods with piecewise constant, discontinuous approximation in time and piecewise linear, continuous approximation in space on strictly acute triangulations. Practical implementations of the present methods are compared to previous schemes which lacked theoretical justification. Numerical results for various model problems are discussed in terms of solution quality and computational costs.

Suggested Citation

  • E. Burman & A. Ern, 2003. "The discrete maximum principle for stabilized finite element methods," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 557-566, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_52
    DOI: 10.1007/978-88-470-2089-4_52
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