A High-Order Finite Element Method for Solving Two-Dimensional Fractional Rayleigh–Stokes Problem for a Heated Generalized Second Grade Fluid

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2024-12-30 DOI:10.1002/fld.5361

Eric Ngondiep

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Abstract

This article develops a high-order finite element scheme in an approximate solution of the two-dimensional Rayleigh–Stokes problem for a heated generalized second-grade fluid with fractional derivatives. The constructed approach consists of approximating the exact solution by interpolation in time while the finite element technique is used in the approximation of the spatial derivatives. This combination is simple and easy to implement. The stability and error estimates of the developed strategy are deeply analyzed in the $L^{\infty}$ -norm. The theoretical studies suggest that the proposed method is unconditionally stable, convergent with order $O (σ^{1 + γ} + h^{p})$ , faster, and more efficient than a broad range of numerical schemes discussed in the literature for the considered time fractional partial differential equation. Some numerical examples are carried out to show the applicability and viability of the new algorithm.

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来源期刊

International Journal for Numerical Methods in Fluids 物理-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

111

审稿时长

8 months

期刊介绍： The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.