Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations

Abstract EN

A finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively.

The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem.

The Diethelm fractional backward difference method (DFBDM), based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs.

The stability and convergence for numerical methods are discussed.

The numerical examples are given to match well with the main conclusions.