A CONTINUOUS SPACE-TIME FINITE-ELEMENT METHOD FOR THE WAVE-EQUATION

The consider a finite element method for the nonhomogeneous second-ord er wave equation, which is formulated in terms of continuous approxima tion functions in both space and time, thereby giving a unified treatm ent of the spatial and temporal discretizations. Our analysis uses pri marily energy arguments, which are quite common for spatial discretiza tions but not for time. We present a priori nodal (in time) superconve rgence error estimates without any special time step restrictions. Our method is based on tensor product spaces for the full discretization.