<div class="csl-bib-body">
<div class="csl-entry">Bonizzoni, F., Braukhoff, M. H., Jüngel, A., & Perugia, I. (2020). A structure-preserving discontinuous Galerkin scheme for the Fisher–KPP equation. <i>Numerische Mathematik</i>, <i>146</i>, 119–157. https://doi.org/10.1007/s00211-020-01136-w</div>
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dc.identifier.issn
0029-599X
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/20271
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dc.description.abstract
An implicit Euler discontinuous Galerkin scheme for the Fisher–Kolmogorov–Petrovsky–Piscounov (Fisher–KPP) equation for population densities with no-flux boundary conditions is suggested and analyzed. Using an exponential variable transformation, the numerical scheme automatically preserves the positivity of the discrete solution. A discrete entropy inequality is derived, and the exponential time decay of the discrete density to the stable steady state in the L1 norm is proved if the initial entropy is smaller than the measure of the domain. The discrete solution is proved to converge in the L2 norm to the unique strong solution to the time-discrete Fisher–KPP equation as the mesh size tends to zero. Numerical experiments in one space dimension illustrate the theoretical results.
en
dc.language.iso
en
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dc.publisher
SPRINGER HEIDELBERG
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dc.relation.ispartof
Numerische Mathematik
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
Fischer-KKP equation
en
dc.subject
Applied Mathematics
en
dc.subject
Computational Mathematics
en
dc.title
A structure-preserving discontinuous Galerkin scheme for the Fisher–KPP equation