C0 Discontinuous Galerkin Methods for a Plate Frictional Contact Problem (Journal of Computational Mathematics, 2018)
Numerous C0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bendingproblem are extended to solve a plate frictional contact problem, which is a fourth-orderelliptic variational inequality of the second kind. This variational inequality contains a non-differentiableterm due to the frictional contact. We prove that these C0 DG methods areconsistent 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; andthe numerical convergence orders confirm the theoretical prediction.