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.
"Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations." Abstr. Appl. Anal. 2013 (SI17) 1 - 10, 2013. https://doi.org/10.1155/2013/857205