典型文献
Discontinuous Galerkin Methods for a Class of Nonvariational Problems
文献摘要：
We extend the finite element method introduced by Lakkis and Pryer(SIAM J.Sci.Com-put.33(2):786-801,2011)to approximate the solution of second-order elliptic problems in nonvariational form to incorporate the discontinuous Galerkin(DG)framework.This is done by viewing the"finite element Hessian"as an auxiliary variable in the formulation.Representing the finite 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 vari-ational elliptic problems.Furthermore,the system matrix is very easy to assemble;thus,this approach greatly reduces the computational complexity of the discretisation compared to the continuous approach.We conduct a stability and consistency analysis making use of the unified frameworkset out in Arnold et al.(SIAM J.Numer.Anal.39(5):1749-1779,2001/2002).We also give an a posteriori analysis of the method in the case where the prob-lem has a strong solution.The analysis applies to any consistent representation of the finite element Hessian,and thus is applicable to the previous works making use of continuous Galerkin approximations.Numerical evidence is presented showing that the method works well also in a more general setting.
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中图分类号：
作者姓名：
Andreas Dedner;Tristan Pryer
作者机构：
Mathematics Institute,University of Warwick,Coventry CV4 7AL,UK;Department of Mathematical Sciences,University of Bath,Bath BA2 7AY,UK
文献出处：
引用格式：
[1]Andreas Dedner;Tristan Pryer-.Discontinuous Galerkin Methods for a Class of Nonvariational Problems)[J].应用数学与计算数学学报,2022(02):634-656
A类：
Nonvariational,Lakkis,Pryer,SIAM,nonvariational,Representing,discretisation,frameworkset
B类：
Discontinuous,Galerkin,Methods,Class,Problems,We,extend,finite,element,introduced,by,Sci,Com,approximate,solution,second,order,elliptic,problems,incorporate,discontinuous,DG,This,done,viewing,Hessian,auxiliary,variable,formulation,setting,yields,linear,system,same,size,having,sparsity,pattern,compact,methods,Furthermore,matrix,very,easy,assemble,thus,this,approach,greatly,reduces,computational,complexity,compared,conduct,stability,consistency,analysis,making,use,unified,out,Arnold,Anal,also,give,posteriori,case,where,has,strong,applies,any,consistent,representation,applicable,previous,approximations,Numerical,evidence,presented,showing,that,well,general
AB值：
0.487486
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