Two-grid IPDG discretization scheme for nonlinear elliptic PDEs

摘要

Two-grid interior penalty discontinuous Galerkin (IPDG) method for the mildly nonlinear second-order elliptic partial differential equations is studied in this paper. The IPDG finite element discretizations are developed and the corresponding well-posedness is established by introducing the equivalent weak formulation of IPDG method and combining Brouwer's fixed point theorem. Some priori error estimates for discrete solution in the broken H-1-norm, L-2-norm and L-infinity-norm are derived, respectively. Two-grid method is designed for solving IPDG discretization scheme and the corresponding error estimate is provided. Numerical experiments are also shown to confirm the efficiency of the proposed approach. (C) 2020 Elsevier B.V. All rights reserved.