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Algebraic Flux Correction for Finite Element Approximation of Transport Equations

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Numerical Mathematics and Advanced Applications

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.

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References

  1. Kuzmin, D, Turek, S.: Flux correction tools for finite elements. J. Comput. Phys. 175, 525–558 (2002)

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics (LS III), University of Dortmund, Vogelpothsweg 87, D-44227, Dortmund, Germany

    Dmitri Kuzmin

Authors
  1. Dmitri Kuzmin
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Editor information

Editors and Affiliations

  1. Departamento de Matemática Aplicada Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706, Santiago de Compostela, Spain

    Alfredo Bermúdez de Castro , Dolores Gómez  & Peregrina Quintela ,  & 

  2. Departamento de Matématica Aplicada, Escola Politécnica Superior, 27002, Lugo, Spain

    Pilar Salgado

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© 2006 Springer

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Kuzmin, D. (2006). Algebraic Flux Correction for Finite Element Approximation of Transport Equations. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_28

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