A continuous space-time finite element method for the wave equation. (English) Zbl 0846.65048
The main purpose of this paper is to demonstrate new variational techniques to analyze the high-order accurate space-time finite element methods for the nonhomogeneous second-order wave equation. The authors prove both global convergence and nodal in time superconvergence error estimates, thereby giving a unified treatment of the spatial and temporal discretization. The method is based on tensor-product spaces for the full discretization. The results of several numerical experiments are given.
Reviewer: P.Chocholatý (Bratislava)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
finite element methods; second-order wave equation; global convergence; superconvergence; error estimatesReferences:
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