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∞(L2) 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) + α/2 in L2(L2) norm, near the maximum age, if u ∈ L2(Wl,2q), where q ≥ 1, 1/2 ≤ l ≤ r + 1, r is the degree of the polynomial of the approximation space, and α is the growth rate of the mortality function; this estimate is super-convergent near the maximum age. Strong stability of the scheme is shown.
hp-DISCONTINUOUS GALERKIN METHODS FOR THE LOTKA-MCKENDRICK EQUATION: A NUMERICAL STUDY
