Discontinuous-continuous Galerkin methods approximate the solution to a population diffusion model with finite life span. The regularity of the solution depends on mortality; it decreases when mortality is high enough. The numerical solution has strong stability and a priori error estimates
are obtained away from the region where the solution is not smooth. The error estimates are optimal in order and in regularity. The matrix Eq. (20) from the discretization satisfies the nonstagnation condition for generalized minimal residual method. Several numerical examples are presented.
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