  We present a new multi-symplectic formulation of constrained Hamiltonian
partial differential equations, and we study the associated local conservation
laws. A multi-symplectic discretisation based on this new formulation is
exemplified by means of the Euler box scheme. When applied to the wave map
equation, this numerical scheme is explicit, preserves the constraint and can
be seen as a generalisation of the Shake algorithm for constrained mechanical
systems. Furthermore, numerical experiments show excellent conservation
properties of the numerical solutions.
