A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate

Klemens Fellner; Victor A Kovtunenko

doi:10.1080/00036811.2015.1105962

A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate

Appl Anal. 2015 Nov 4;95(12):2661-2682. doi: 10.1080/00036811.2015.1105962. eCollection 2016.

Authors

Klemens Fellner¹, Victor A Kovtunenko^{1

2}

Affiliations

¹ Institute of Mathematics and Scientific Computing, University of Graz, NAWI Graz, 8010Graz, Austria.
² Lavrent'ev Institute of Hydrodynamics, 630090Novosibirsk, Russia.

Abstract

A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.

Keywords: 35B27; 35J60; 78A57; 82B24; Boltzmann statistics; Electro-kinetic; Robin condition; error corrector; homogenisation; interfacial jump; nonlinear Poisson equation; oscillating coefficients; steady-state Poisson–Nernst–Planck system.