Weak Galerkin finite element methods for the Darcy equation
Date
2018
Authors
Wang, Zhuoran, author
Liu, Jiangguo, advisor
Tavener, Simon, advisor
Donahue, Tammy, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
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 interiors and on edges might be different. The discrete weak gradients specified in the local Raviart-Thomas spaces are used to approximate the classical gradients. The WG finite element method has nice features, e.g., locally mass conservation, continuous normal fluxes and easy implementation. Numerical experiments on quadrilateral and hybrid meshes are presented to demonstrate its good approximation and expected convergence rates. We discuss the extension of WG finite element methods to three-dimensional domains.