摘要
本文针对2维和3维对流-扩散-反应方程的界面问题提出了一种基于非贴体网格的扩展杂交间断有限元方法.该方法在单元的内部分别用分片k(k≥1)和m(m=k,k-1)次多项式逼近标量函数及其梯度,在单元边界上用k次多项式逼近标量函数的迹,在界面上则用界面单元内部的k次多项式在界面上的限制去逼近标量函数的迹.对于弱问题,本文利用Lax-Milgram定理证明其解的存在唯一性.对于离散格式,本文给出了其解的存在唯一性以及能量范数下的最优误差估计.
This paper proposes an extended hybridizable discontinuous Galerkin(HDG)finite element for 2D and 3D convection-diffusion-reaction equation interface problems on body-unfitted meshes.This finite element uses piecewise polynomials of degrees k(k≥1)and m(m=k,k-1)to approximate the scalar function and its gradient respectively in the interior of elements,piecewise polynomials of degrees k to approximate the traces of the scalar function on the inter-element boundaries inside the sub-domains and constraints on the interface of piecewise polynomials of degrees k inside interface elements to approximate the traces of the scalar function on the interface.The existence and uniqueness of weak solution for the weak problem and discrete solution for the discrete scheme are proved respectively.Lax-Milgram theorem is used for the weak problem.The optimal error estimation is derived in the energy norm for the discrete scheme.
作者
王慧媛
陈豫眉
WANG Hui-Yuan;CHEN Yu-Mei(School of Mathematics,Sichuan University,Chengdu 610064,China;College of Mathematics Education,China West Normal University,Nanchong 637009,China)
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2023年第2期27-35,共9页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金(11971094)。
