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

@article{Lscher2021NumericalRF, title={Numerical results for an unconditionally stable space-time finite element method for the wave equation}, author={Richard L{\"o}scher and Olaf Steinbach and Marco Zank}, journal={ArXiv}, year={2021}, volume={abs/2103.04324} }

In this work, we introduce a new space-time variational formulation of the secondorder wave equation, where integration by parts is also applied with respect 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. We consider a conforming tensor-product approach with piecewise polynomial, continuous basis functions, which results…

## One Citation

A generalized inf-sup stable variational formulation for the wave equation

- Mathematics, Computer ScienceArXiv
- 2021

This new approach is based on a suitable extension of the ansatz space to include the information of the differential operator of the wave equation at the initial time t = 0, which allows it to prove unique solvability in a subspace ofH1(Q) with Q being the space–time domain.

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This new approach is based on a suitable extension of the ansatz space to include the information of the differential operator of the wave equation at the initial time t = 0, which allows it to prove unique solvability in a subspace ofH1(Q) with Q being the space–time domain.

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