C0 Discontinuous Galerkin Methods for a Plate Frictional Contact Problem

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.