A space-time discontinuous Galerkin method for the solution of the wave equation in the time domain.

*(English)*Zbl 1183.76813Summary: In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the wave equation. We present a space-time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the homogeneous wave equation. The use of hierarchical wave-like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space-time finite element methods.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76Q05 | Hydro- and aero-acoustics |

##### Keywords:

wave equation; discontinuous Galerkin; Lagrange multipliers; medium frequency; wave basis functions; space-time finite elements
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\textit{S. Petersen} et al., Int. J. Numer. Methods Eng. 78, No. 3, 275--295 (2009; Zbl 1183.76813)

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