In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L 1 approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L 2 -norm with optimal order of convergence O ( h 2 + τ 2 − α ) where τ and h are time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.
KeywordsTime-Fractional Nonlinear Fourth-Order Diffusion Equation with Time DelayFinite Volume Element MethodCaputo-Fractional DerivativeOptimal Priori Error Analysis
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