论文标题
针对时间依赖的泊松 - 尼斯特·普朗克方程的虚拟元素方法的错误分析
Error Analysis of Virtual Element Methods for the Time-dependent Poisson-Nernst-Planck Equations
论文作者
论文摘要
我们讨论并分析了有关时间依赖性泊松静脉planck方程的一般多边形网格的虚拟元素方法，该方程是一种非线性耦合系统，广泛用于半导体和离子通道。空间离散化基于椭圆形预测和$ l^2 $投影操作员，并且为时间离散化，使用了向后的Euler方案。提出了半离散方案后，我们在$ l^2 $和$ h^1 $规范中得出了先验错误估计。最后，一个数值实验验证了理论收敛的结果。
We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck equations, which are a nonlinear coupled system widely used in semiconductors and ion channels. The spatial discretization is based on the elliptic projection and the $L^2$ projection operator, and for the temporal discretization, the backward Euler scheme is employed. After presenting the semi and fully discrete schemes, we derive the a priori error estimates in the $L^2$ and $H^1$ norms. Finally, a numerical experiment verifies the theoretical convergence results.
