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A Stabilized Space–Time Finite Element Method for the Wave Equation

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 128)

Abstract

We consider a space–time variational formulation of the wave equation by including integration by parts also in the time variable. A standard finite element discretization by using lowest order piecewise linear continuous functions then requires a CFL condition to ensure stability. To overcome this restriction, and following the work of Zlotnik (Convergence rate estimates of finite-element methods for second-order hyperbolic equations. In: Numerical methods and applications, pp. 155–220. CRC, Boca Raton, 1994), we consider, in the case of tensor–product space–time discretizations, a stabilized variational problem which is unconditionally stable. We provide a stability and error analysis, and some numerical results which confirm the theoretical findings.

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Correspondence to Olaf Steinbach .

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Steinbach, O., Zank, M. (2019). A Stabilized Space–Time Finite Element Method for the Wave Equation. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-14244-5_17

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