Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 341, Issue -, Pages 61-79Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2018.04.003
Keywords
Poisson-Nernst-Planck/Stokes coupling; Mixed finite element method; Taylor-Hood element; Semi-discretization; Full discretization; The optimal error estimate
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Funding
- National Natural Science Foundation of China [11401150]
- NSF [DMS-1418806]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1418806] Funding Source: National Science Foundation
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In this paper, a type of mixed finite element method is developed to solve the Poisson-Nernst-Planck/Stokes coupling problem which is adopted to model charged fluids through the transport coupling between Stokes equations of an incompressible fluid and Poisson Nernst-Planck (PNP) equations of a diffuse charge system. The Taylor-Hood (Pk+1Pk) mixed element is employed to discretize both mixed Poisson equations and Stokes equations, and the standard P-k finite element is used to discretize Nernst-Planck equations. Optimal convergence rates for both the electrostatic potential and ionic concentrations of PNP equations are obtained in both L-2 and H-1 norms, simultaneously, optimal convergence rates are also obtained for the velocity and pressure of Stokes equations in [H-1](d) and L-2 norm, respectively. Numerical experiments validate the theoretical results. (C) 2018 Elsevier B.V. All rights reserved.
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