ABSTRACT
The mathematical simulation of an aquifer system’s hydraulic behavior requires the analytical or numerical integration of two simultaneous partial differential equations, called governing equations, ensuing from the simultaneous application of energy and mass conservation principles to pseudo-continuous subsystems of groundwater systems. Domains typified by simple structures and properties encourage analytical solutions, but for most groundwater problems, particularly for fractured rocks, a closed analytical solution does not exist. Dirichlet and Neumann prescriptions are typically the most common boundary conditions to guarantee unique groundwater flow solutions in a state of equilibrium: steady-state solutions. Two properties of the elementary analytical solutions of the continuity equation help to select efficient base functions. Continuous integrations of low order elementary analytical solutions generate a natural linear set of base functions. A Taylor series expansion defined in a closed interval can also be written as a general polynomial.
