Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 12, pp. 1-22.

Title: Fully discrete Galerkin schemes for the nonlinear and
       nonlocal Hartree equation
   
Author: Walter H. Aschbacher (Technische Univ., Munchen, Germany)

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.
 
Submitted September 26, 2008. Published January 12, 2009.
Math Subject Classifications: 35Q40, 35Q35, 35J60, 65M60, 65N30.
Key Words: Hartree equation; quantum many-body system; 
           weakly nonlinear dispersive waves; Newtonian gravity;  
	   Galerkin theory; finite element methods; 
	   discretization accuracy.