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Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes
Barrenechea, Gabriel Burman, Erik Karakatsani, Fotini
Barrenechea, Gabriel
Burman, Erik
Karakatsani, Fotini
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EPub Date
Publication Date
2016-05-07
Submitted Date
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Abstract
For the case of approximation of convection–diffusion equations using
piecewise affine continuous finite elements a new edge-based nonlinear diffusion
operator is proposed that makes the scheme satisfy a discrete maximum principle.
The diffusion operator is shown to be Lipschitz continuous and linearity preserving.
Using these properties we provide a full stability and error analysis, which, in the diffusion
dominated regime, shows existence, uniqueness and optimal convergence. Then
the algebraic flux correction method is recalled and we show that the present method
can be interpreted as an algebraic flux correction method for a particular definition of
the flux limiters. The performance of the method is illustrated on some numerical test
cases in two space dimensions.
Citation
Barrenechea, G., Burman, E. & Karakatsani, F. (2016). Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes. Numerische Mathematik, 135(2), 521-545. http://dx.doi.org/10.1007/s00211-016-0808-z
Publisher
Springer
Journal
Numerische Mathematik
Research Unit
DOI
10.1007/s00211-016-0808-z
PubMed ID
PubMed Central ID
Type
Article
Language
en
Description
The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-016-0808-z
Series/Report no.
ISSN
0029-599X
EISSN
0945-3245