The classical wave equation, as the chief example of second order hyperbolic equations, is considered on a bounded convex domain. Then a continuous Galerkin method, based on piecewise linear polynomials both in space and time, is applied, and stability estimates for a slightly more general problem are obtained. These are used to prove optimal order a priori error estimates with minimal regularity assumptions on the solution. Other techniques, to prove optimal order of convergence, are compared.
