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We present and analyze a new space-time finite element method for thesolution of neural field equations with transmission delays. The numericaltreatment of these systems is rare in the literature and currently has severalrestrictions on the spatial domain and the functions involved, such asconnectivity and delay functions. The use of a space-time discretization, withbasis functions that are discontinuous in time and continuous in space(dGcG-FEM), is a natural way to deal with space-dependent delays, which isimportant for many neural field applications. In this article we provide adetailed description of a space-time dGcG-FEM algorithm for neural delayequations, including an a-priori error analysis. We demonstrate the applicationof the dGcG-FEM algorithm on several neural field models, including problemswith an inhomogeneous kernel.

A space-time finite element method for neural field equations with transmission delays