Galerkin Methods in Age and Space for a Population Model with Nonlinear Diffusion

Abstract

We present Galerkin methods in both the age and space variables for an age-dependent population undergoing nonlinear diffusion. The methods presented are a generalization of the methods presented in {\it A Variable Time Step Method for an Age-dependent Population Model with Nonlinear Diffusion}, where the approximation space in age was taken to be the space of piecewise constant functions. In this paper, we allow the use of discontinuous piecewise polynomial subspaces of $L^2$ as the approximation space in age. As in the piecewise constant case, we move the discretization along characteristic lines. The time variable has been left continuous. The methods are shown to be superconvergent in the age variable.