A mortar finite element approximation for the linear Poisson-Boltzmann equation
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.
scientific article; zbMATH DE number 2165257