A Second Order Time Accurate Finite Volume Scheme for the Time-Fractional Diffusion Wave Equation on General Nonconforming Meshes
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SUSHI (Scheme Using Stabilization and Hybrid Interfaces) is a finite volume method has been developed at the first time to approximate heterogeneous and anisotropic diffusion problems. It has been applied later to approximate several types of partial differential equations. The main feature of SUSHI is that the control volumes can only be assumed to be polyhedral. Further, a consistent and stable Discrete Gradient is developed.
In this note, we establish a second order time accurate implicit scheme for the TFDWE (Time Fractional Diffusion-Wave Equation). The space discretization is based on the use of SUSHI whereas the time discretization is performed using a uniform mesh. The scheme is based on the use of an equivalent system of two low order equations. We sketch the proof of the convergence of the stated scheme. The convergence is unconditional. This work is an improvement of  in which a first order scheme, whose convergence is conditional, is established.
KeywordsFinite volume Time Fractional Diffusion Wave Equation System Unconditional convergence Second order time accurate
- 3.Bradji, A.: Some convergence results of a multi-dimensional finite volume scheme for a time-fractional diffusion-wave equation. In: Cancès, C., Omnes, P. (eds.) FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol. 199, pp. 391–399. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57397-7_32CrossRefzbMATHGoogle Scholar