Weak Galerkin finite element methods for the Darcy equation
The Darcy equation models pressure-driven flow in porous media. Because of the importance of ground water flow in oil recovery and waste mitigation, several types of numerical methods have been developed for solving the Darcy equation, such as continuous Galerkin finite element methods (CGFEMs) and mixed finite element methods (MFEMs). This thesis describes the lowest-order weak Galerkin (WG) finite element method to solve the Darcy equation and compares it to those well-known methods. In this method, we approximate the pressure by constants inside elements and on edges. Pressure values in ...
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Liu, Jiangguo; Tavener, Simon