The virtual element method for solving two-dimensional fractional cable equation on general polygonal meshes

Abstract

In this paper, the conforming virtual element method (VEM) is considered to solve the two-dimensional fractional cable equation involving two Riemann–Liouville fractional derivatives. We adopt the Backward Euler Method and the classical scheme for the numerical discrete scheme of the time derivative. Meanwhile, the conforming VEM, which is generated for arbitrary order of accuracy and the arbitrary polygonal meshes, is analysed for the discretization of the spatial direction. Based on the energy projection operator, the fully discrete formula is proved to be unconditionally stable, and the optimal convergence results are derived with regard to the -norm in detail. Finally, some numerical experiments are implemented to verify the theoretical results.