Geodesic
Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation
Electronic journal of differential equations, Tome 2009 (2009)
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.
Classification : 35Q40, 35Q35, 35J60, 65M60, 65N30
Keywords: Hartree equation, quantum many-body system, weakly nonlinear dispersive waves, Newtonian gravity, Galerkin theory, finite element methods, discretization accuracy 
@article{EJDE_2009__2009__a195,
     author = {Aschbacher,  Walter H.},
     title = {Fully discrete {Galerkin} schemes for the nonlinear and nonlocal {Hartree} equation},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1173.35642},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a195/}
}
TY  - JOUR
AU  - Aschbacher,  Walter H.
TI  - Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation
JO  - Electronic journal of differential equations
PY  - 2009
VL  - 2009
UR  - http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a195/
LA  - en
ID  - EJDE_2009__2009__a195
ER  - 
%0 Journal Article
%A Aschbacher,  Walter H.
%T Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation
%J Electronic journal of differential equations
%D 2009
%V 2009
%U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a195/
%G en
%F EJDE_2009__2009__a195
Aschbacher,  Walter H. Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a195/