Approximate solutions to Poisson-Boltzmann systems with Sobolev gradients

Authors:
Abdul Majid;Sultan Sial
Affiliations:
Mathematics Department, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt., Pakistan;Mathematics Department, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt., Pakistan
Venue:
Journal of Computational Physics
Year:
2011

Citing 6
Cited 1

Energy minimization using Sobolev gradients: application to phase separation and ordering

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Constructing fair curves and surfaces with a Sobolev gradient method

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Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals

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Preconditioning operators and Sobolevgradients for nonlinear elliptic problems

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Application of Sobolev gradient method to Poisson-Boltzmann system

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Numerical approximation of time evolution related to Ginzburg-Landau functionals using weighted Sobolev gradients

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Abstract

A weighted Sobolev gradient approach [1] is presented to a nonlinear PBE [2] with discontinuous coefficient functions. A comparison is given between the weighted and unweighted Sobolev gradient in the finite element setting in two and three dimensions. Behavior of the various Sobolev gradients is discussed for large jump size in the coefficient. A comparison with Newton's method is given where the failure of Newton's method is demonstrated for a test problem.