Finite element methods of an operator splitting applied to population balance equations
In population balance equations, the distribution of the entities depends not only on space and time but also on their own properties. The operator splitting method is used to transform the time-dependent problem into two unsteady subproblems of a smaller complexity. The first subproblem is a time-dependent convection-diffusion problem while the second one is a transient transport problem with pure advection. The authors use the backward Euler method to discretize the subproblems in time. Since the first problem is convection-dominated, the local projection method is applied as stabilization in space. The main result is the unconditional stability of the method and derivation of optimal error estimates. Numerical tests are used to confirm the theoretical results.
time-dependent convection-diffusion problem
scientific article; zbMATH DE number 5991222
scientific article