论文标题
无条件的积极性保留和泊松方程的能量耗散方案
Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations
论文作者
论文摘要
我们为泊松方程开发了一组数字方案。我们证明我们的计划是大规模保守的，可以解决的独特性，并且无条件地保持积极性。此外，一阶方案被证明是无条件的能量耗散性的。这些属性具有各种空间离散化。给出了数值结果以验证这些特性。此外，数值结果表明二阶方案也是能量耗散的，一阶和二阶方案都保留了方程满足最大原理的情况的最大原理。
We develop a set of numerical schemes for the Poisson--Nernst--Planck equations. We prove that our schemes are mass conservative, uniquely solvable and keep positivity unconditionally. Furthermore, the first-order scheme is proven to be unconditionally energy dissipative. These properties hold for various spatial discretizations. Numerical results are presented to validate these properties. Moreover, numerical results indicate that the second-order scheme is also energy dissipative, and both the first- and second-order schemes preserve the maximum principle for cases where the equation satisfies the maximum principle.
