The spreading adoption of computationally intensive techniques such as Reverse Time Migration and Full Waveform Inversion increases the need of efficiently solving the three-dimensional wave equation. Common finite-difference discretization schemes lose their accuracy and efficiency in complex geological settings with discontinuities in the material properties and topography. Finite elements on tetrahedral meshes follow the interfaces while maintaining their accuracy and can have smaller meshes if the elements are scaled with the velocity. Here, we consider two higher-order finite element methods that allow for explicit time stepping: the continuous mass-lumped finite-element method (CMLFE) and the symmetric interior penalty discontinuous Galerkin method (SIPDG). The price paid for the ability to perform explicit time stepping is an increase in computational cost: CMLFE requires a larger number of discretization nodes to preserve accuracy, whereas SIPDG needs additional fluxes to impose the continuity of the solution. Therefore, it is not obvious which one is more efficient. We compare the two methods in terms of accuracy, stability and computational cost. Experiments on a three-dimensional problem with a dipping interface show that CMLFE and SIPDG have similar stability conditions, accuracy and efficiency, the last being measured as the computational time required to reach a given accuracy of the result.
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