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arXiv · 2312.00291

The Existence the Solution of Nonlinear Discrete Schemes and Convergence of a Linearized Iterative Method for time-dependent PNP Equations

Yang Liu·Shi Shu·Ying Yang
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Abstract

We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method respectively that the stiffness matrix is a column M-matrix under certain conditions, and then the existence theory of these three FE nonlinear fully discrete solutions is presented by using Brouwer's fixed point theorem. Second, the contraction of a commonly used linearized iterative method-Gummel iteration is proven, and then the convergence theory is established for the iteration. At last, a numerical experiment is shown to verifies the theories.

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Yang Liu, Shi Shu, Ying Yang. 2023-12-01. The Existence the Solution of Nonlinear Discrete Schemes and Convergence of a Linearized Iterative Method for time-dependent PNP Equations. https://arxiv.org/abs/2312.00291

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