Domain transformation methods are useful techniques for solving problems on non-stationary domains. In this work, we consider the evolution of the water table in an unconfined aquifer. This nonlinear, time-dependent problem is greatly simplified by using a mapping from the physical domain to a reference domain and is then further reduced to a single, (nonlinear) partial differential equation. We show well-posedness of the approach and propose a stable and convergent discretization scheme. Numerical results are presented supporting the theory.
- Domain tranformation
- Water table evolution
- Finite element method
Boon, W. M., Balbarini, N., Binning, P. J., & Nordbotten, J. M. (2017). Efficient water table evolution discretization using domain transformation. Computational Geosciences, 21(1), 3-11. https://doi.org/10.1007/s10596-016-9597-9