Abstract
For the second–order wave equation, we compare the Newmark Galerkin method with a stabilised space–time finite element method for tensor–product space–time discretisations with piecewise multilinear, continuous ansatz and test functions leading to an unconditionally stable Galerkin–Petrov scheme, which satisfies a space–time error estimate. We show that both methods require to solve a linear system with the same system matrix. In particular, the stabilised space–time finite element method can be solved sequentially in time as the Newmark Galerkin method. However, the treatment of the right–hand side of the wave equation is different, where the Newmark Galerkin method requires more regularity.
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Acknowledgements
The author greatly appreciates the discussion with I. Perugia, J. Schöberl and P. Stocker.
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Zank, M. (2021). The Newmark Method and a Space–Time FEM for the Second–Order Wave Equation. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_122
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DOI: https://doi.org/10.1007/978-3-030-55874-1_122
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