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Volume 37, Issue 2
C0 Discontinuous Galerkin Methods for a Plate Frictional Contact Problem

Fei Wang, Tianyi Zhang & Weimin Han

DOI: 10.4208/jcm.1711-m2017-0187

J. Comp. Math., 37 (2019), pp. 184-200.

Published online: 2018-09

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  • 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.

  • Keywords

Variational inequality of fourth-order, Discontinuous Galerkin method, Plate frictional contact problem, Optimal order error estimate.

  • AMS Subject Headings

65N30, 49J40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

feiwang.xjtu@xjtu.edu.cn (Fei Wang)

tianyi.zhang1106@gmail.com (Tianyi Zhang)

weimin-han@uiowa.edu (Weimin Han)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-184, author = {Wang , FeiZhang , Tianyi and Han , Weimin}, title = {C0 Discontinuous Galerkin Methods for a Plate Frictional Contact Problem}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1711-m2017-0187}, url = {http://global-sci.org/intro/article_detail/jcm/12676.html} }
TY - JOUR T1 - C0 Discontinuous Galerkin Methods for a Plate Frictional Contact Problem AU - Wang , Fei AU - Zhang , Tianyi AU - Han , Weimin JO - Journal of Computational Mathematics VL - 2 SP - 184 EP - 200 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1711-m2017-0187 UR - https://global-sci.org/intro/article_detail/jcm/12676.html KW - Variational inequality of fourth-order, Discontinuous Galerkin method, Plate frictional contact problem, Optimal order error estimate. AB -

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.

Fei Wang, Tianyi Zhang & Weimin Han. (2019). C0 Discontinuous Galerkin Methods for a Plate Frictional Contact Problem. Journal of Computational Mathematics. 37 (2). 184-200. doi:10.4208/jcm.1711-m2017-0187
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