Some convergence results of a multi-dimensional finite volume scheme for a time-fractional diffusion-wave equation

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∞ (L2)–error estimate.