Consistent finite difference operators that satisfy \(\nabla \cdot \nabla \times =0\) (Q1122338)

The problems associated with constructing finite difference operators in noncartesian geometry that satisfy \(\nabla \cdot \nabla \times =0\) are investigated. The final result is given for cylindrical geometry, any interior boundary fitted coordinate system and a wider spectrum of problems which is based on the fact that any above mentioned coordinate system has at least one coordinate singularity where the inverse mapping to cartesian coordinate system is one to one.