Convergent Finite Element Discretizations of the Navier-stokes-nernst-planck-poisson System

Global Existence and Asymptotic Behavior of Self - Similar Solutions for the Navier - Stokes - Nernst - Planck - Poisson System in R 3

Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes

The performance of multigrid methods for the standard Poisson problem and for the consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes equations is investigated. It is demonstrated that overlapping additive Schwarz methods are effective smoothers, provided that the solution in the overlap region is weighted by the inverse counting matrix. It is also shown ...

Modeling studies and numerical analyses of coupled PDEs system in electrohydrodynamics

MODELING STUDIES AND NUMERICAL ANALYSES OF COUPLED PDES SYSTEM IN ELECTROHYDRODYNAMICS by Yuzhou Sun Dr. Pengtao Sun, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas, USA Electrohydrodynamics (EHD) is the term used for the hydrodynamics coupled with electrostatics, whose governing equations consist of the electrostatic potential (Poisson) equation,...

An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations

Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources, which describe the electrodiffusion of ions in a solvated biomolecular system. In this paper, some error bounds for a piecewise finite element approximation to this problem are derived. S...

A Scalable Auxiliary Space Preconditioner for High-order Finite Element Methods

In this paper, we revisit an auxiliary space preconditioning method proposed by Xu [Computing 56, 1996], in which low-order finite element spaces are employed as auxiliary spaces for solving linear algebraic systems arising from high-order finite element discretizations. We provide a new convergence rate estimate and parallel implementation of the proposed algorithm. We show that this method is...