TY - JOUR
T1 - A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation
AU - Naldi, Giovanni
AU - Cavalli, Fausto
PY - 2010
Y1 - 2010
N2 - In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with Neumann boundary conditions involving recent mass transportation methods. The numerical scheme is based on an alternative formulation of the problem using the so called pseudo-inverse of the cumulative distribution function. We establish a stable fully discrete scheme that inherits the energy dissipation and mass conservation from the associated continuous problem. We perform some numerical experiments which confirm our results.
AB - In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with Neumann boundary conditions involving recent mass transportation methods. The numerical scheme is based on an alternative formulation of the problem using the so called pseudo-inverse of the cumulative distribution function. We establish a stable fully discrete scheme that inherits the energy dissipation and mass conservation from the associated continuous problem. We perform some numerical experiments which confirm our results.
KW - Cahn-Hilliard equation
KW - Pseudo-inverse function
KW - Stable numerical methods for fourth order equations
KW - Cahn-Hilliard equation
KW - Pseudo-inverse function
KW - Stable numerical methods for fourth order equations
UR - http://hdl.handle.net/10807/85483
U2 - 10.3934/krm.2010.3.123
DO - 10.3934/krm.2010.3.123
M3 - Article
SN - 1937-5093
VL - 3
SP - 123
EP - 142
JO - Kinetic and Related Models
JF - Kinetic and Related Models
ER -