The presented article contains a 3D mesh generation routine optimized with
the Metropolis algorithm. The procedure enables to produce meshes of a
prescribed volume V_0 of elements. The finite volume meshes are used with the
Finite Element approach. The FEM analysis enables to deal with a set of coupled
nonlinear differential equations that describes the electrodiffusional problem.
Mesh quality and accuracy of FEM solutions are also examined. High quality of
FEM type space-dependent approximation and correctness of discrete
approximation in time are ensured by finding solutions to the 3D Laplace
problem and to the 3D diffusion equation, respectively. Their comparison with
analytical solutions confirms accuracy of obtained approximations.