Discontinuous Galerkin methods for the Lotka-McKendrick equation with finite life-span

We consider a model of population dynamics whose mortality function is unbounded and the solution is not regular near the maximum age. A continuous-time discontinuous Galerkin method to approximate the solution is described and analyzed. Our results show that the scheme is convergent, in L-infinity (L-2) norm, at the rate of r + 1/2 away from the maximum age and that it is convergent at the rate of l - 1/(2q) + alpha/2 in L-2 (L-2) norm, near the maximum age, if u is an element of L-2(W-l,W-2q), where q >= 1, 1/2 <= l <= r + 1, r is the degree of the polynomial of the approximation space, and alpha is the growth rate of the mortality function; this estimate is super-convergent near the maximum age. Strong stability of the scheme is shown.