## 5 Discretized Governing Equations and Solution Procedure

The governing equations of Section 3 which are already in a weak form are discretized in space by means of the FEM and the discrete fracture model of Section 4.7 is implemented.

The following approximations are used for the field variables

$\left\{\begin{array}{l}\mathbf{u}={\mathbf{N}}_{u}\overline{\mathbf{u}}\\ {p}^{w}={\mathbf{N}}_{\mathit{cp}}{\overline{\mathbf{p}}}^{w}\\ T={\mathbf{N}}_{T}\overline{\mathbf{T}}\end{array}\right)$

(4.45)

where N_{α}, α = u, p, T are the shape functions and $\overline{\mathbf{u}},{\overline{\mathbf{p}}}^{w},\overline{\mathbf{T}}$ the nodal values of the field variables.

Space discretization of Eqs. (4.14), (4.17), (4.18) and (4.22), incorporating the constitutive equations, results in the ...