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The Finite Element Method
Element Families and Interpolation Functions
Finite Element Simulation of Isothermal Flow in Porous
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algorithm application approach aquifer assumed basis functions boundary conditions boundary element method collocation collocation method computed consider convergence coordinate Darcy's law defined denote derived described difference approximation displacement domain dt dt dx dx dXj dXj element equations element matrix evaluated finite difference methods finite element method flow equation flow problems fluid flow flux formulation fracture free surface Galerkin given global matrix governing equation Green's Green's function Green's theorem grid groundwater flow Huyakorn hydraulic conductivity hydraulic head increment initial iteration linear matrix equation medium multiphase flow Newton-Raphson nodal values node nonlinear numerical obtain one-dimensional parameters partial differential equations phase Pinder polynomial porous media prescribed pressure region reservoir reservoir simulation saturation scheme shape functions shown in Fig simulation solve Substituting Eq subsurface transport equation trial function two-dimensional typical unknown variable vector velocity vertical written yields