A Space-Time Finite Element Method for Neural Field Equations with Transmission Delays

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    Abstract

    We present and analyze a new space-time nite element method for the solution
    of neural eld 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 functionsinvolved, 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 eld applications. In
    this paper 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 eld models, including problems with an inhomogeneous kernel.
    Original languageEnglish
    Pages (from-to)B797–B818
    JournalSIAM journal on scientific computing
    Volume39
    Issue number5
    DOIs
    Publication statusPublished - 21 Dec 2017

    Keywords

    • Neural fields
    • Transmission delays
    • Discontinuous Galerkin finite element methods
    • Space-time methods

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