C<sup>0</sup> Discontinuous Galerkin Methods for a Plate Frictional Contact Problem

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 Cdiscontinuous 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

Tianyi Zhang

Weimin Han

  1. Numerical methods for static shallow shells lying over an obstacle

    Piersanti, Paolo | Shen, Xiaoqin

    Numerical Algorithms, Vol. 85 (2020), Iss. 2 P.623

    https://doi.org/10.1007/s11075-019-00830-7 [Citations: 10]
  2. Unconditional stability and optimal error estimates of discontinuous Galerkin methods for the second-order wave equation

    He, Limin | Han, Weimin | Wang, Fei | Cai, Wentao

    Applicable Analysis, Vol. 100 (2021), Iss. 6 P.1143

    https://doi.org/10.1080/00036811.2019.1636968 [Citations: 2]
  3. The interior penalty virtual element method for the fourth-order elliptic hemivariational inequality

    Qiu, Jiali | Wang, Fei | Ling, Min | Zhao, Jikun

    Communications in Nonlinear Science and Numerical Simulation, Vol. 127 (2023), Iss. P.107547

    https://doi.org/10.1016/j.cnsns.2023.107547 [Citations: 1]
  4. Discontinuous Galerkin methods for solving a hyperbolic inequality

    Wang, Fei | Han, Weimin

    Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 3 P.894

    https://doi.org/10.1002/num.22330 [Citations: 1]
  5. A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality

    Wang, Fei | Shah, Sheheryar | Xiao, Wenqiang

    BIT Numerical Mathematics, Vol. 61 (2021), Iss. 3 P.1005

    https://doi.org/10.1007/s10543-021-00848-1 [Citations: 6]
  6. Nonconforming virtual element methods for the fourth-order variational inequalities of the first kind

    Qiu, Jiali | Zhao, Jikun | Wang, Fei

    Journal of Computational and Applied Mathematics, Vol. 425 (2023), Iss. P.115025

    https://doi.org/10.1016/j.cam.2022.115025 [Citations: 3]
  7. Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem

    Wang, Fei | Zhao, Jikun

    IMA Journal of Numerical Analysis, Vol. 41 (2021), Iss. 2 P.1496

    https://doi.org/10.1093/imanum/draa005 [Citations: 19]
  8. Discontinuous Galerkin Methods for Solving a Frictional Contact Problem with Normal Compliance

    Xiao, Wenqiang | Wang, Fei | Han, Weimin

    Numerical Functional Analysis and Optimization, Vol. 39 (2018), Iss. 12 P.1248

    https://doi.org/10.1080/01630563.2018.1472609 [Citations: 5]
  9. On a family of discontinuous Galerkin fully-discrete schemes for the wave equation

    He, Limin | Han, Weimin | Wang, Fei

    Computational and Applied Mathematics, Vol. 40 (2021), Iss. 2

    https://doi.org/10.1007/s40314-021-01423-8 [Citations: 1]
  10. 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, Feifei

    Journal of Computational and Applied Mathematics, Vol. 371 (2020), Iss. P.112700

    https://doi.org/10.1016/j.cam.2019.112700 [Citations: 19]