ABSTRACT

In this paper, we discuss the virtual element formulation for the nonlinear convection–diffusion–reaction equation. We consider the Streamline upwind Petrov–Galerkin stabilization to reduce the non-physical oscillations presented in the solution. The nonlinear term is evaluated after a suitable modification with the help of a polynomial projection operator. We perform the error analysis by showing the existence of the solution and derive the convergence estimates in the energy norm. Numerical experiments are conducted in order to validate the theoretical results.

中文翻译：

---

多边形网格上非线性对流-扩散-反应方程的虚拟元方法

摘要

在本文中，我们讨论非线性对流-扩散-反应方程的虚拟元公式。我们考虑 Streamline 逆风 Petrov-Galerkin 稳定以减少解决方案中出现的非物理振荡。在多项式投影算子的帮助下，在适当修改后评估非线性项。我们通过显示解的存在性来进行误差分析，并推导出能量范数中的收敛估计。进行数值实验以验证理论结果。