A mortar finite element approximation for the linear Poisson-Boltzmann equation (Q1774840)

The authors develop a numerical method for the linear Poisson-Boltzmann equation \(-\nabla\cdot (\varepsilon (x)\nabla\phi (x))+\kappa (x)\phi (x)=\sum_{i=1}^Kq_i\delta (x-x_i)\), where \(\delta\) denotes the Dirac distribution and \(\varepsilon (x)\) is the dielectric potential. After introducing a weak formulation for this equation, the authors justify the existence of a solution. Next, a special mortar condition is constructed to deal with the jumps of the solution and coefficients. In the last part of the paper the authors establish the convergence of numerical approximations.