For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. I...For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.展开更多
A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discon...A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discontinuous functions. In this paper, we derive the optimal order error estimate in L2 norm based on dual argument. Numerical experiment is conducted to confirm the theoretical results.展开更多
In this paper,we solve linear parabolic integral differential equations using the weak Galerkin finite element method(WG)by adding a stabilizer.The semidiscrete and fully-discrete weak Galerkin finite element schemes ...In this paper,we solve linear parabolic integral differential equations using the weak Galerkin finite element method(WG)by adding a stabilizer.The semidiscrete and fully-discrete weak Galerkin finite element schemes are constructed.Optimal convergent orders of the solution of the WG in L^(2) and H^(1) norm are derived.Several computational results confirm the correctness and efficiency of the method.展开更多
基金Acknowldgements. The authors would like to express their sincere thanks to the editor and referees for their very helpful comments and suggestions, which greatly improved the quality of this paper. We also would like to thank Dr. Xiu Ye for useful discussions. The first author＇s research is partially supported by the Natural Science Foundation of Shandong Province of China grant ZR2013AM023, the Project Funded by China Postdoctoral Science Foundation no. 2014M560547, the Fundamental Research Funds of Shandong University no. 2015JC019, and NSAF no. U1430101.
文摘For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.
基金The authors thank the referees and the editor for their invaluable comments and suggestions which have helped to improved the paper greatly. Also, the authors would like to thank Prof. Xiu Ye for useful discussions and Dr. Paul Scott for helpful revision. This work is done when the first author is visiting Department of Mathematics and Statistics, University of Arkansas at Little Rock under supported by the State Scholarship Fund from the China Scholarship Council. The first author＇s research is partially supported by the Natural Science Foundation of Shandong Province of China grant ZR2013AM023, ZR2012AM019.
文摘A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discontinuous functions. In this paper, we derive the optimal order error estimate in L2 norm based on dual argument. Numerical experiment is conducted to confirm the theoretical results.
基金supported in part by China Natural National Science Foundation(No.11901015)and China Postdoctoral Science Foundation(Nos.2018M640013 and 2019T120008)The research of Ran Zhang was supported in part by China Natural National Science Foundation(Nos.91630201,U1530116,11726102,11771179,93K172018Z01,11701210,JJKH20180113KJ and 20190103029JH)by the Program for Cheung Kong Scholars of Ministry of Education of China,Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education.
文摘In this paper,we solve linear parabolic integral differential equations using the weak Galerkin finite element method(WG)by adding a stabilizer.The semidiscrete and fully-discrete weak Galerkin finite element schemes are constructed.Optimal convergent orders of the solution of the WG in L^(2) and H^(1) norm are derived.Several computational results confirm the correctness and efficiency of the method.
