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Algebraic Flux Correction for Finite Element Approximation of Transport Equations

In: Numerical Mathematics and Advanced Applications

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  • Dmitri Kuzmin

    (University of Dortmund, Institute of Applied Mathematics (LS III))

Abstract

An algebraic approach to the design of high-resolution finite element schemes for convection-dominated flows is pursued. It is explained how to get rid of nonphysical oscillations and remove excessive artificial diffusion in regions where the solution is sufficiently smooth. To this end, the discrete transport operator and the consistent mass matrix are modified so as to enforce the positivity constraint in a mass-conserving fashion. The concept of a target flux and a new definition of upper/lower bounds make it possible to design a general-purpose flux limiter which provides an optimal treatment of both stationary and time-dependent problems.

Suggested Citation

  • Dmitri Kuzmin, 2006. "Algebraic Flux Correction for Finite Element Approximation of Transport Equations," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 345-353, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_28
    DOI: 10.1007/978-3-540-34288-5_28
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