Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation (Communications in Computational Physics, 2018)
This paper is devoted to the error estimate for the iterative discontinuousGalerkin (IDG) method introduced in [P. Yin, Y. Huang and H. Liu. Commun. Comput.Phys. 16: 491–515, 2014] to the nonlinear Poisson-Boltzmann equation. The total errorincludes both the iteration error and the discretization error of the direct DG methodto linear elliptic equations. For the DDG method, the energy error is obtained by aconstructive approach through an explicit global projection satisfying interface conditionsdictated by the choice of numerical fluxes. The $L^2$ error of order O(hm+1) forpolynomials of degree m is further recovered. The bounding constant is also shownto be independent of the iteration times. Numerical tests are given to validate theestablished convergence theory.