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On space enrichment estimator for nonlinear Poisson-Boltzmann

: Randrianarivony, M.


Simos, T.; Psihoyios, G.; Tsitouras, C.:
11th International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2013 : Rhodes, Greece, September 21-27, 2013
Woodbury, N.Y.: AIP, 2013 (AIP Conference Proceedings 1558)
ISBN: 978-0-7354-1184-5
International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) <11, 2013, Rhodes>
Fraunhofer SCAI ()

We consider the mathematical aspect of the nonlinear Poisson-Boltzmann equation which physically governs the ionic interaction between solute and solvent media. The presented a-posteriori estimates can be computed locally in a very efficient manner. The a-posteriori error is based upon hierarchical space enrichment which ensures its efficiency and reliability. A brief survey of the solving of the nonlinear system resulting from the FEM discretization is reported. To corroborate the analysis, we report on a few numerical results for illustrations. We numerically examine some values of the constants encountered in the theoretical study.