- Research Article
1
- 10.3390/fractalfract9080481
A Mixed Finite Volume Element Method for Nonlinear Time Fractional Fourth-Order Reaction–Diffusion Models
- Jul 23, 2025
- Fractal and Fractional
- Jie Zhao + 2 more +2
In this paper, a linearized mixed finite volume element (MFVE) scheme is proposed to solve the nonlinear time fractional fourth-order reaction–diffusion models with the Riemann–Liouville time fractional derivative. By introducing an auxiliary variable σ=Δu, the original fourth-order model is reformulated into a lower-order coupled system. The first-order time derivative and the time fractional derivative are discretized by using the BDF2 formula and the weighted and shifted Grünwald difference (WSGD) formula, respectively. Then, a fully discrete MFVE scheme is constructed by using the primal and dual grids. The existence and uniqueness of a solution for the MFVE scheme are proven based on the matrix theories. The scheme’s unconditional stability is rigorously derived by using the Gronwall inequality in detail. Moreover, the optimal error estimates for u in the discrete L∞(L2(Ω)) and L2(H1(Ω)) norms and for σ in the discrete L2(L2(Ω)) norm are obtained. Finally, three numerical examples are given to confirm its feasibility and effectiveness.
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