A conforming virtual element method for Emden-Fowler model over polygonal meshes

The primary goal of this article is to propose an efficient virtual element method formulation for solving a two-dimensional time-fractional Emden-Fowler model. The virtual element technique is a generalization of the finite element approach to polygonal and polyhedral meshes in the Galerkin approximation framework. A fully discrete virtual element scheme is obtained by using a fractional version of the Grünwald-Letnikov approximation for the temporal discretization and the virtual element method for the spatial discretization. We establish the existence and uniqueness of the discrete solution, that is, the well-posedness of the approach. The error analysis and optimal convergence order with respect to the \(L^2-\)norm and the \(H^1-\)seminorm are presented. The numerical experiments validated the theoretical analysis and demonstrated the technique’s efficacy on convex and non-convex polygonal meshes.