Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation
This paper is devoted to the error estimate for the iterative discontinuous Galerkin (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 error includes both the iteration error and the discretization error of the direct DG method to linear elliptic equations. For the DDG method, the energy error is obtained by a constructive approach through an explicit global projection satisfying interface conditions dictated by the choice of numerical fluxes. The $L^2$ error of order O(hm+1) for polynomials of degree m is further recovered. The bounding constant is also shown to be independent of the iteration times. Numerical tests are given to validate the established convergence theory.
