Discontinuous Bubble Immersed Finite Element Method for Poisson-Boltzmann Equation (Communications in Computational Physics, 2018)
We develop a numerical scheme for nonlinear Poisson-Boltzmann equation.First, we regularize the solution of PBE to remove the singularity. We introduce thediscontinuous bubble function to treat the nonhomogeneous jump conditions of theregularized solution. Next, starting with an initial guess, we apply linearization totreat the nonlinearity. Then, we discretize the discontinuous bubble and the bilinearform of PBE. Finally, we solve the discretized linear problem by IFEM. This process isrepeated by updating the previous approximation. We carry out numerical experiments. We observe optimal convergence rate for allexamples.