A class of well-posed approximations for constrained second order hyperbolic equations

The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The principle is a singular modification of the mass matrix obtained by the mean of different discretizations of the solution and of its time derivative. The major interest of these methods is that the semi-discretized problem is well-posed and energy conserving. Numerical experiments show that this is a crucial property to build stable numerical schemes.