Local Averaging Type a Posteriori Error Estimates for the Nonlinear Steady-state Poisson-Nernst-Planck Equations
Ying Yang, Ruigang Shen, Mingjuan Fang, Shi Shu
TL;DR
This paper develops local averaging a posteriori error estimates for nonlinear steady-state Poisson-Nernst-Planck equations, providing reliable bounds and confirming their effectiveness through numerical experiments.
Contribution
It introduces a novel local averaging approach for a posteriori error estimation in nonlinear Poisson-Nernst-Planck equations, with proven reliability and efficiency.
Findings
Global upper bounds of error estimators established
Local lower bounds of error estimators derived
Numerical experiments confirm estimator reliability
Abstract
The a posteriori error estimates are studied for a class of nonlinear stead-state Poisson-Nernst-Planck equations, which are a coupled system consisting of the Nernst-Planck equation and the Poisson equation. Both the global upper bounds and the local lower bounds of the error estimators are obtained by using a local averaging operator. Numerical experiments are given to confirm the reliability and efficiency of the error estimators.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Computational Fluid Dynamics and Aerodynamics · Numerical methods in inverse problems