5
Finite Element Methods for Solving
Hydrodynamic Dispersion Equations
5.1 Finite Element Methods for Two-Dimensional
Problems
5.1.1 The Weighted Residual M ethod
Consider the following two-dimensional advection-dispersion equation
(5.1.1)
which is subject to the initial condition
C(x, y, 0) = f, (x, y) E (R),
(5.1.2)
boundary conditions
C(X,y,t) = gl' (x,y) E (r1)'
(5.1.3)
and
(5.1.4)
where (R) is the flow domain, (rd and (r 2 ) are boundary sections of (R), f is
a given function in (R), gl and g2 are given functions along (r 1 ) and (r 2 ),
respectively, and n x and ny are components of the unit outer normal vector to
the boundary (r2)' Equation (5.1.3) expresses the boundary condition of
given concentration, i.e., the first-type boundary condition, while Eq. (5.1.4)
expresses the boundary condition of given dispersion flux, i.e., the secondtype boundary condition.
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