Automatic time stepping with global error control for groundwater flow models

Automatic time stepping with global error control is proposed for the time integration of the diffusion equation to simulate groundwater flow in confined aquifers. The scheme is based on an a posteriori error estimate for the discontinuous Galerkin finite-element methods. A stability factor is involved in the error estimate and it is used to adapt the time step and control the global temporal error for the backward Euler method. The stability factor can be estimated by solving a dual problem. The stability factor is not sensitive to the accuracy of the dual solution and the overhead computational cost can be minimized by solving the dual problem using large time steps. Numerical experiments are conducted to show the application and the performance of the automatic time stepping scheme. Implementation of the scheme can lead to improvements in accuracy and efficiency of groundwater flow models.