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In this work, we introduce a new space-time variational formulation of thesecond-order wave equation, where integration by parts is also applied withrespect to the time variable, and a modified Hilbert transformation is used.For this resulting variational setting, ansatz and test spaces are equal. Thus,conforming finite element discretizations lead to Galerkin--Bubnov schemes. Weconsider a conforming tensor-product approach with piecewise polynomial,continuous basis functions, which results in an unconditionally stable method,i.e., no CFL condition is required. We give numerical examples for a one- and atwo-dimensional spatial domain, where the unconditional stability and optimalconvergence rates in space-time norms are illustrated.

Numerical results for an unconditionally stable space-time finite element method for the wave equation