Scholarlink

<p>The issue we address in this paper is to propose a virtual element analysis for the nonlinear Hallaire equation as a modified version of the nonlinear diffusion equation with a time-fractional derivative. The spatial direction is discretized by the virtual element method. The upper limit of error related to the solution of the space-discrete scheme and the exact solution is obtained. To get an optimal error estimate, the mesh-graded time discretization approach is employed to approximate the Caputo fractional derivative. Also, a second-order technique is used to approximate the nonlinear terms. Then, a fully-discrete scheme is constructed. The unconditional stability and order of convergence of the presented numerical formulation are proved in separate theorems. Finally, two test problems examined the theoretical results of this paper.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Error estimate of virtual element approximation for loaded time-fractional Hallaire’s equation

  • 期刊论文

  • 发表日期：

    2025年2月10日

查看全文
  • Mostafa Abbaszadeh,
  • Mehdi Dehghan

摘要

The issue we address in this paper is to propose a virtual element analysis for the nonlinear Hallaire equation as a modified version of the nonlinear diffusion equation with a time-fractional derivative. The spatial direction is discretized by the virtual element method. The upper limit of error related to the solution of the space-discrete scheme and the exact solution is obtained. To get an optimal error estimate, the mesh-graded time discretization approach is employed to approximate the Caputo fractional derivative. Also, a second-order technique is used to approximate the nonlinear terms. Then, a fully-discrete scheme is constructed. The unconditional stability and order of convergence of the presented numerical formulation are proved in separate theorems. Finally, two test problems examined the theoretical results of this paper.