C<sup>0</sup> Discontinuous Galerkin Methods for a Plate Frictional Contact Problem
Year: 2019
Author: Fei Wang, Tianyi Zhang, Weimin Han
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 184–200
Abstract
Numerous C0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second kind. This variational inequality contains a non-differentiable term due to the frictional contact. We prove that these C0 DG methods are consistent and stable, and derive optimal order error estimates for the quadratic element. A numerical example is presented to show the performance of the C0 DG methods; and the numerical convergence orders confirm the theoretical prediction.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1711-m2017-0187
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 2 : pp. 184–200
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Variational inequality of fourth-order Discontinuous Galerkin method Plate frictional contact problem Optimal order error estimate.
Author Details
Fei Wang Email
Tianyi Zhang Email
Weimin Han Email
-
Nonconforming finite element method for a 4th-order history-dependent hemivariational inequality
Qiu, Jiali | Ling, Min | Wang, Fei | Wu, BangminCommunications in Nonlinear Science and Numerical Simulation, Vol. 145 (2025), Iss. P.108750
https://doi.org/10.1016/j.cnsns.2025.108750 [Citations: 0] -
Numerical methods for static shallow shells lying over an obstacle
Piersanti, Paolo | Shen, XiaoqinNumerical Algorithms, Vol. 85 (2020), Iss. 2 P.623
https://doi.org/10.1007/s11075-019-00830-7 [Citations: 12] -
Unconditional stability and optimal error estimates of discontinuous Galerkin methods for the second-order wave equation
He, Limin | Han, Weimin | Wang, Fei | Cai, WentaoApplicable Analysis, Vol. 100 (2021), Iss. 6 P.1143
https://doi.org/10.1080/00036811.2019.1636968 [Citations: 2] -
The interior penalty virtual element method for the fourth-order elliptic hemivariational inequality
Qiu, Jiali | Wang, Fei | Ling, Min | Zhao, JikunCommunications in Nonlinear Science and Numerical Simulation, Vol. 127 (2023), Iss. P.107547
https://doi.org/10.1016/j.cnsns.2023.107547 [Citations: 3] -
Discontinuous Galerkin methods for solving a hyperbolic inequality
Wang, Fei | Han, WeiminNumerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 3 P.894
https://doi.org/10.1002/num.22330 [Citations: 1] -
A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality
Wang, Fei | Shah, Sheheryar | Xiao, WenqiangBIT Numerical Mathematics, Vol. 61 (2021), Iss. 3 P.1005
https://doi.org/10.1007/s10543-021-00848-1 [Citations: 6] -
Nonconforming virtual element methods for the fourth-order variational inequalities of the first kind
Qiu, Jiali | Zhao, Jikun | Wang, FeiJournal of Computational and Applied Mathematics, Vol. 425 (2023), Iss. P.115025
https://doi.org/10.1016/j.cam.2022.115025 [Citations: 4] -
Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem
Wang, Fei | Zhao, JikunIMA Journal of Numerical Analysis, Vol. 41 (2021), Iss. 2 P.1496
https://doi.org/10.1093/imanum/draa005 [Citations: 21] -
Discontinuous Galerkin Methods for Solving a Frictional Contact Problem with Normal Compliance
Xiao, Wenqiang | Wang, Fei | Han, WeiminNumerical Functional Analysis and Optimization, Vol. 39 (2018), Iss. 12 P.1248
https://doi.org/10.1080/01630563.2018.1472609 [Citations: 5] -
On a family of discontinuous Galerkin fully-discrete schemes for the wave equation
He, Limin | Han, Weimin | Wang, FeiComputational and Applied Mathematics, Vol. 40 (2021), Iss. 2
https://doi.org/10.1007/s40314-021-01423-8 [Citations: 1] -
Adaptive discontinuous Galerkin methods for solving an incompressible Stokes flow problem with slip boundary condition of frictional type
Wang, Fei | Ling, Min | Han, Weimin | Jing, FeifeiJournal of Computational and Applied Mathematics, Vol. 371 (2020), Iss. P.112700
https://doi.org/10.1016/j.cam.2019.112700 [Citations: 19]