Implicit and semi-implicit second-order time stepping methods for the Richards equation

This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations based on standard or mixed finite element methods. Different implicit semi-implicit temporal discretization of second-order accuracy studied. To obtain a linear system schemes, we propose using extrapolation formulas and/or Taylor approximations nonlinear terms. A convergence series tests performed to analyze efficiency robustness schemes. developed scheme, proposed formulation involving saturation pressure head Lagrange element, performs better than other schemes flux Raviart-Thomas elements. scheme is good alternative when meet issues.