Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations

Abstract In this article, a finite volume element method with the second-order weighted and shifted Grünwald difference (WSGD) formula is proposed and studied for nonlinear time fractional mobile/immobile transport equations on triangular grids. By using the WSGD formula of approximating the Riemann–Liouville fractional derivative and an interpolation operator I h ∗ $I_{h}^{*}$ , a second-order fully discrete finite volume element (FVE) scheme is formulated. The existence, uniqueness, and unconditional stability for the fully discrete FVE scheme are derived, the optimal a priori error estimates in L ∞ ( L 2 ( Ω ) ) $L^{\infty }(L^{2}(\varOmega))$ and L 2 ( H 1 ( Ω ) ) $L^{2}(H^{1}(\varOmega))$ norms are obtained, in which the convergence orders are independent of the fractional parameters. At the end of this article, two numerical examples with different nonlinear terms are given to verify the feasibility and effectiveness.