Title: A space-time finite element method for neural field equations with transmission delays,
Abstract: We present and analyze a new space-time finite element method for the
solution of neural field equations with transmission delays. The numerical
treatment of these systems is rare in the literature and currently has several
restrictions on the spatial domain and the functions involved, such as
connectivity and delay functions. The use of a space-time discretization, with
basis functions that are discontinuous in time and continuous in space
(dGcG-FEM), is a natural way to deal with space-dependent delays, which is
important for many neural field applications. In this article we provide a
detailed description of a space-time dGcG-FEM algorithm for neural delay
equations, including an a-priori error analysis. We demonstrate the application
of the dGcG-FEM algorithm on several neural field models, including problems
with an inhomogeneous kernel.