Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation
arXiv:0812.3606
Abstract
We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.
25 pages, 1 figure