Abstract
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 H1-norm, L2-norm and L∞-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.
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