The internal bending moment (m) is continuous throughout the element , but in general is discontinuous at element interfaces in the mesh (since concentrated moments can be added at the nodes) and is described by a linear polynomial within each element. The internal bending moment has a piecewise linear variation, meaning each element in the mesh may be described by a different linear polynomial, depending on it's geometric properties, material properties, loading and constraints.
Discontinuity caused by a concentrated moment being applied at node 2.