Abstract
We present an implicit finite volume scheme for a linear time-fractional diffusion-wave equation using the discrete gradient introduced in Eymard et al. (IMA J Numer Anal 30:1009–1043, 2010, [2]). A convergence order for the error between the gradient of the exact solution and the discrete gradient of the approximate solution is proved. This yields an \(L^\infty (L^2)\)–error estimate.
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References
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Bradji, A. (2017). Some Convergence Results of a Multi-dimensional Finite Volume Scheme for a Time-Fractional Diffusion-Wave Equation. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_32
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DOI: https://doi.org/10.1007/978-3-319-57397-7_32
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