An extended P1-nonconforming finite element method on general polytopal partitions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:381

Article

Liu, Yujie^1,2  Wang, Junping³ 

[1] Peng Cheng Lab, Ctr Quantum Comp, Shenzhen 518005, Peoples R China

[2] Huazhong Univ Sci & Technol, Ctr Math Sci, Wuhan, Peoples R China

[3] Natl Sci Fdn, Div Math Sci, Alexandria, VA 22314 USA

关键词: Convection-diffusion-reaction equations;    P-1-nonconforming method;    Polytopal partition;    Weak Galerkin;    Finite element methods;    Error estimates;   

DOI  :  10.1016/j.cam.2020.113021

来源: Elsevier

【 摘 要 】

An extended P-1-nonconforming finite element method is developed in this article for the Dirichlet boundary value problem of convection-diffusion-reaction equations on general polytopal partitions. This new method was motivated by the simplified weak Galerkin method, and makes use of only the degrees of freedom on the boundary of each element and, hence, has reduced computational complexity. Numerical stability and optimal order of error estimates in H-1 and L-2 norms are established for the corresponding numerical solutions. Some numerical results are presented to computationally verify the mathematical convergence theory. A superconvergence phenomenon on rectangular partitions is noted and illustrated through various numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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