The Existence the Solution of Nonlinear Discrete Schemes and Convergence of a Linearized Iterative Method for time-dependent PNP Equations
Numerical Analysis
2023-12-04 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2312.00291,
title = {The Existence the Solution of Nonlinear Discrete Schemes and Convergence of a Linearized Iterative Method for time-dependent PNP Equations},
author = {Yang Liu and Shi Shu and Ying Yang},
journal= {arXiv preprint arXiv:2312.00291},
year = {2023}
}