Discontinuous Galerkin method for piecewise regular solutions to the nonlinear age-structured population model

A discontinuous Galerkin approximation of the nonlinear Lotka–McKendrick equation is considered in the frequent case when the solution is only piecewise regular. An O(hr+1/2)O(hr+1/2) error estimate for rth order polynomial finite elements is proved, as well as piecewise H1-regularity of the exact solution which guarantees the error estimate for r = 0. Certain implementational details which improve the robustness of the method are also addressed.