Contributions to Books:
A. Jüngel, S. Schuchnigg:
"Entropy- dissipating semi-discrete Runge-Kutta schemes for non-linear diffusion schemes";
in: "ASC Report 26/2015",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Semi-discrete Runge-Kutta schemes for nonlinear diffusion equations of parabolic type are analyzed. Conditions are determined under which the schemes dissipate the discrete entropy locally. The dissipation property is a consequence of the concavity of the diﬀerence of the entropies at two consecutive time steps. The concavity property is shown to be related to the Bakry-Emery approach and the geodesic convexity of the entropy. The abstract conditions are veriﬁed for quasilinear parabolic equations (including the porous-medium equation), a linear diffusion system, and the fourth-order quantum diffusion equa-tion. Numerical experiments for various Runge-Kutta ﬁnite-difference discretizations of the one-dimensional porous-medium equation show that the entropy-dissipation property is in fact global.
Entropy-dissipative numerical schemes, Runge-Kutta schemes, entropy method,
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.