Kelvin-Voigt方程的不连续Galerkin压力校正格式分析

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-15 DOI:10.1016/j.cnsns.2025.109263

Kushal Roy, Rajen Kumar Sinha

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引用次数: 0

摘要

我们提出并分析了一种求解Kelvin-Voigt的不连续伽辽金压力校正方案。证明了该方案是无条件稳定的。通过L2范数和DG范数的先验误差估计建立了离散速度的收敛性，并通过数值实验验证了我们的发现。理论分析证实了DG范数的最优收敛率和L2范数的最优空间精度，尽管时间精度似乎不是最优的。然而，数值实验表明，该方案在时间和空间上都具有最佳精度。

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Analysis of a discontinuous Galerkin pressure correction scheme for the Kelvin-Voigt equation

We formulate and analyze a discontinuous Galerkin pressure correction scheme for solving the Kelvin-Voigt. The proposed scheme is proven to be unconditionally stable. Convergence of the discrete velocity is established through a priori error estimates in

L^{2}

and

D G

norms, and validating our findings through numerical experiments. The theoretical analysis confirms optimal convergence rates in the

D G

norm, and optimal spatial accuracy in the

L^{2}

norm, though temporal accuracy appears suboptimal. Nevertheless, numerical experiments indicate that the scheme achieves optimal accuracy in both time and space.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.