Negative norm estimates for fully discrete finite element approximations to the wave equation with nonhomogeneous \(L_2\) Dirichlet boundary data. (English) Zbl 0920.65058
Summary: This paper treats time and space finite element approximations of the solution to the nonhomogeneous wave equation with \(L_2\) boundary terms and smooth right-hand side. For the case of \(L_2\) 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.
MSC:
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35L05 | Wave equation |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
