标题： 一种满足自由能的间断伽辽金方法用于一维泊松-纳尔斯特-普朗克系统 显示英文标题

标题： A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systems

摘要： 我们设计了一种任意阶的自由能满足的不连续伽辽金（DG）方法，用于求解时变泊松-纳尔斯特-普朗克系统。半离散和全离散DG方法都被证明对于正的数值解满足相应的离散自由能耗散定律。通过参考正的单元平均值，采用一种保持精度的限制器来保证数值解的正性。给出了数值例子以展示数值算法的高分辨率，并说明了质量守恒、自由能耗散以及稳态保持等已证明的性质。 显示英文摘要

摘要： We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivities of numerical solutions are enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.