The concentration is approximated over the finite element as follows:

(9–8)

where:

{N} = element shape functions

{C_e} = nodal concentration vector (input/output as CONC)

The application of the variational principle and finite element approximation Equation 9–8 to Equation 9–6 produces the matrix equation as:

(9–9)

where:

= element diffusion damping matrix

= element diffusion conductivity matrix

= element transport conductivity matrix

= element diffusion flux load vector

= element diffusing substance generation load vector

vol = element volume

S = element surface

= nodal diffusion flow rate vector applied to the element (input/output as RATE on F command)

The finite element Equation 9–9 is unsymmetric. To keep the equation symmetric, the transport effects can be applied as a load vector by setting KEYOPT(2) = 1 for the diffusion elements (PLANE238, SOLID239, SOLID240). Using this option activates a nonlinear solution, and at least two iterations are required to achieve a response to the transport effects.