## Continuous-time finite element analysis of multiphase flow in groundwater hydrology.(English)Zbl 0847.76030

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.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76T99 Multiphase and multicomponent flows 76S05 Flows in porous media; filtration; seepage 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 86A05 Hydrology, hydrography, oceanography
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