Continuous-time finite element analysis of multiphase flow in groundwater hydrology

Abstract

A nonlinear differential equation describing an air-water system in groundwater hydrology is studied. The system is presented in a fractional flow formulation, while a continuous-time version of the finite element method is developed and analyzed for the approximation of the saturation and pressure. More specifically, the saturation equation is treated numerically by a Galerkin finite element method, and the pressure equation is analyzed by a mixed finite element method.