Algebraic Flux Correction for Finite Element Approximation of Transport Equations

Dmitri Kuzmin ()
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Dmitri Kuzmin: University of Dortmund, Institute of Applied Mathematics (LS III)

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 345-353 from Springer

Abstract: 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.

Keywords: Positivity Constraint; Solid Body Rotation; Discrete Maximum Principle; Consistent Mass Matrix; Lump Mass Matrix (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_28

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DOI: 10.1007/978-3-540-34288-5_28

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