The discrete maximum principle for stabilized finite element methods

  • E. Burman
  • A. Ern


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.


Isotropic Diffusion Discrete Maximum Principle Maximum Overshoot Nonlinear Source Term Local Mesh Size 
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Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • E. Burman
    • 1
  • A. Ern
    • 2
  1. 1.Ecole Polytechnique Federale de LausanneDMALausanneSwitzerland
  2. 2.CERMICSEcole Nationale des Ponts et Chaussées (ENPC)Marne la ValléeFrance

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