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.