Negative norm estimates for fully discrete finite element approximations to the wave equation with nonhomogeneous 𝐿₂ Dirichlet boundary data

Abstract

This paper treats time and space finite element approximations of the solution to the nonhomogeneous wave equation with L 2 {L_2} boundary terms and smooth right-hand side. For the case of L 2 {L_2} boundary data, the rates of convergence in negative norms are derived. In the case of smooth forcing term and zero boundary data, optimal rates of convergence in "positive" norms are provided.