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(h(r+1/2)) error estimate for rth order polynomial finite elements is proved, as well as piecewise H(1)-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.
Krzyzanowski
Piotr
P
Warsaw University, Institute of Applied Mathematics, Banacha 2, 02-097 Warszawa, Poland. przykry@mimuw.edu.pl
Wrzosek
Dariusz
D
Wit
Dominik
D
D000818:Animals; D003621:Daphnia / Q000254:growth & development; D020342:Finite Element Analysis; D005399:Fishes / Q000254:growth & development; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics; D011235:Predatory Behavior