Error estimates for discontinuous Galerkin finite element methods for a neuron network model

Abstract

A nonlinear partial integro-differential equation, modeling neuron networks, has been considered. We approximate the model by using piecewise polynomials in space. We establish the boundedness and the invertibility of the model operator. We study the order of accuracy of a finite element approximation (in space) of the model with a full Galerkin inner product as well as with a quadrature inner product considering the solutions are in and in each subdomain such that .

Keywords:

• Integro-differential equation
• numerical approximation
• error estimates

AMS Subject Classifications:

• 65M12
• 65M15