A Mixed Finite Element Method for Solving the Time-Fractional-Darcy Equation

Darcy flow is an important mathematical model to describe a fluid through a porous media. Many research reveal fractional model is an alternative approach to simulate the porous medium flow. To seek more accurate mathematical model for this type of flow, a novel Time-Fractional-Darcy equation is investigated and numerically solved in this paper. The finite difference method is utilized to discrete the temporal fractional derivative. For pursuing higher calculate accuracy and better numerical stability, the fully coupled mixed finite element methods with stabilized terms are proposed in space. The effectiveness and accuracy of the presented methodology are consistently demonstrated by 2D and 3D numerical examples.