%0 Journal Article
%T The Finite Volume Element Method for Time-Fractional Nonlinear Fourth-Order Diffusion Equation with Time Delay
%A Anran Li
%A Qing Yang
%J Engineering
%P 53-72
%@ 1947-394X
%D 2025
%I Scientific Research Publishing
%R 10.4236/eng.2025.171004
%X 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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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 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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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 are time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.
%K Time-Fractional Nonlinear Fourth-Order Diffusion Equation with Time Delay
%K Finite Volume Element Method
%K Caputo-Fractional Derivative
%K Optimal Priori Error Analysis
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140058