Discontinuous Galerkin Methods for a Class of Nonvariational Problems

作     者：Andreas Dedner Tristan Pryer Andreas Dedner;Tristan Pryer

作者机构：Mathematics InstituteUniversity of WarwickCoventry CV47ALUK Department of Mathematical SciencesUniversity of BathBath BA27AYUK 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2022年第4卷第2期

页      面：634-656页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Nonvariational problems Discontinuous Galerkin Error estimates Adaptivity 

摘      要：We extend the fnite element method introduced by Lakkis and Pryer(SIAM ***.33(2):786–801,2011)to approximate the solution of second-order elliptic problems in nonvariational form to incorporate the discontinuous Galerkin(DG)*** is done by viewing the“fnite element Hessianas an auxiliary variable in the *** the fnite element Hessian in a discontinuous setting yields a linear system of the same size and having the same sparsity pattern of the compact DG methods for variational elliptic ***,the system matrix is very easy to assemble;thus,this approach greatly reduces the computational complexity of the discretisation compared to the continuous *** conduct a stability and consistency analysis making use of the unifed frameworkset out in Arnold et al.(SIAM ***.39(5):1749–1779,2001/2002).We also give an a posteriori analysis of the method in the case where the problem has a strong *** analysis applies to any consistent representation of the fnite element Hessian,and thus is applicable to the previous works making use of continuous Galerkin *** evidence is presented showing that the method works well also in a more general setting.