A discontinuous Galerkin(DG)scheme for solving semilinear elliptic problem is developed and analyzed in this paper.The DG finite element discretization is first established,then the corresponding well-posedness is pro...A discontinuous Galerkin(DG)scheme for solving semilinear elliptic problem is developed and analyzed in this paper.The DG finite element discretization is first established,then the corresponding well-posedness is provided by using Brouwer’s fixed point method.Some optimal priori error estimates under both DG norm and L^(2)norm are presented,respectively.Numerical results are given to illustrate the efficiency of the proposed approach.展开更多
基金The second and third authors are supported by the National Natural Science Foundation of China(No.12071160)the Guangdong Basic and Applied Basic Research Foundation(No.2019A1515010724)+2 种基金The second author is also supported by the National Natural Science Foundation of China(No.11671159)The third author is also supported by National Natural Science Foundation of China(No.12101250)the Science and Technology Projects in Guangzhou(No.202201010644).
文摘A discontinuous Galerkin(DG)scheme for solving semilinear elliptic problem is developed and analyzed in this paper.The DG finite element discretization is first established,then the corresponding well-posedness is provided by using Brouwer’s fixed point method.Some optimal priori error estimates under both DG norm and L^(2)norm are presented,respectively.Numerical results are given to illustrate the efficiency of the proposed approach.
