论文标题
Fokker的有限批量离散量的一致性和收敛性 - Planck操作员
Consistency and convergence for a family of finite volume discretizations of the Fokker--Planck operator
论文作者
论文摘要
我们为Fokker（Planck Operator）介绍了各种有限体积离散化方案的家族，其特征是边缘上的重量功能不同。这个家族特别包括建立了良好的scharfetter-甘穆尔离散以及最近开发的方形近似（SQRA）方案。我们从数值和建模的角度来激发了这个离散化家族，并提供了统一的一致性和错误分析。我们的主要结果表明，收敛顺序主要取决于网格的质量，第二位是权重质量。我们通过数值实验表明，对于小梯度，离散化家族的最佳代表的选择是高度不平凡的，而对于大型梯度，scharfetter-与其他渐变相比，gummel方案脱颖而出。
We introduce a family of various finite volume discretization schemes for the Fokker--Planck operator, which are characterized by different weight functions on the edges. This family particularly includes the well-established Scharfetter--Gummel discretization as well as the recently developed square-root approximation (SQRA) scheme. We motivate this family of discretizations both from the numerical and the modeling point of view and provide a uniform consistency and error analysis. Our main results state that the convergence order primarily depends on the quality of the mesh and in second place on the quality of the weights. We show by numerical experiments that for small gradients the choice of the optimal representative of the discretization family is highly non-trivial while for large gradients the Scharfetter--Gummel scheme stands out compared to the others.
