Entropy-dissipating semi-discrete Runge-Kutta schemes for nonlinear diffusion equations
Entropy-dissipating semi-discrete Runge-Kutta schemes for nonlinear diffusion equations
复制标题
非线性扩散方程的熵耗散半离散龙格-库塔格式
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Stefan Schuchnigg
中科院分区：
文献类型：
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作者：
A. Jungel;Stefan Schuchnigg
研究了抛物型非线性扩散方程的半离散Runge-Kutta格式。条件下，该计划耗散的离散熵局部确定。耗散性质是在两个连续的时间步长的熵差的乘积的结果。该性质被证明是有关的Bakry-Emery方法和测地凸的熵。对拟线性抛物方程（包括多孔介质方程）、线性扩散系统和四阶量子扩散方程的抽象条件进行了验证。一维多孔介质方程的各种Runge-Kutta有限差分离散的数值实验表明，熵耗散属性实际上是全局的。
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 equation. 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.
影响因子：
1.7
作者：
A. Jüngel;D. Matthes
通讯作者：
A. Jüngel;D. Matthes