Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

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.

Keywords

• Hartree equation
• quantum many-body system
• weakly nonlinear dispersive waves
• Newtonian gravity
• Galerkin theory
• finite element methods
• discretization accuracy