It is not clear to me that the condition that the constraint system be well posed is the one needed for considering a system free of this problem. First because well posedness as such is not enough to guarantee the possibility of a numerical scheme: The system could be well posed but still depart exponentially from the constraint sub-manifold, thus making impossible any reliable calculation. So the non-principal part of the system must also be considered, and probably suitably modified in the neighborhood of the constraint sub-manifold. Second, since one is never solving, or simulating, the constraint evolution equations, that is, they play no role in the scheme, why should one consider them at all? I think the emphasis should be put on guaranteeing a numerical scheme without spurious solutions; because, as argued above, uniqueness should imply that the constraints are satisfied. Thus, what seems to be needed is a connection between well posedness, or rather no exponential departure from the constraint sub-manifold, and lack of spurious solutions on the numerical schema.
© Max Planck Society and the author(s)