A structure-preserving discontinuous Galerkin scheme for the Fischer-KPP equation
Francesca Bonizzoni,
Marcel Braukhoff,
Ansgar Jüngel
et al.
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 L 1 norm is proved if the initial entropy is smalle… Show more
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