Pure Mathematics
E-print 5, 2007
Author(s):
S. H. Christiansen
Title:
Constraint preserving schemes for some gauge invariant wave equations
Abstract:
We study discretizations of the Maxwell-Klein-Gordon equation
as an example of a constrained geometric non-linear evolution partial
differential equation. For the temporal gauge we propose a fully discrete
scheme which preserves the non-linear constraint thanks to a special
application of Lagrange multipliers. We show that the method generalizes
to Hamiltonian wave equations whose kinetic and potential
energy are both invariant under a group of transformations,
even though the Galerkin spaces are not invariant.
We then extend the method to the Lorenz gauge.
Numerical results illustrate the discussion.
A pdf version of the entire e-print.