TY - JOUR
T1 - Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation
AU - Peimeng Yin, Yunqing Huang & Hailiang Liu
JO - Communications in Computational Physics
VL - 1
SP - 168
EP - 197
PY - 2018
DA - 2018/01
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2016-0226
UR - https://global-sci.org/intro/article_detail/cicp/10524.html
KW - Poisson-Boltzmann equation, DG methods, global projection, energy error estimates, $L^2$ error estimates.
AB - <p style="text-align: justify;">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 $L^2$<sup>&nbsp;</sup>error of order O(h<sup>m+1</sup>) 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.</p>