A systematic study on weak Galerkin finite element method for second-order parabolic problems

被引：10
|
作者：
Deka, Bhupen [1 ,2 ]
Kumar, Naresh [1 ]
机构：
[1] Indian Inst Technol Guwahati, Dept Math, Gauhati, India
[2] Indian Inst Technol Guwahati, Dept Math, Gauhati 781039, India
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 03期
基金：
中国国家自然科学基金;
关键词：
convergence analysis; discrete weak gradient; parabolic problems; semidiscrete and fully discrete schemes; weak Galerkin finite element method; DISCONTINUOUS GALERKIN; EQUATION SUBJECT; INTERFACE PROBLEMS; TIME;
D O I：
10.1002/num.22973
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present work, we have described a systematic numerical study on weak Galerkin (WG) finite element method for second-order linear parabolic problems by allowing polynomial approximations with various degrees for each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in L infinity (L2) and L infinity (H1) norms for a general WG element (Pk(K), Pj(??????K), [Pl(K)]2), where k > 1, j > 0 and l > 0 are arbitrary integers. The fully discrete space-time discretization is based on a first order in time Euler scheme. Numerical experiments are reported to justify the robustness, reliability and accuracy of the WG finite element method.
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页码：2444 / 2474
页数：31
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