Higher order discontinuous Galerkin finite element methods for the contact problems

Abstract

In this chapter, we study the a posteriori error analysis of higher order discontinuous Galerkin finite element methods for two contact problems, namely, the obstacle problem and the Signorini problem. The reliability and efficiency of proposed a posteriori error estimators are discussed. An appropriate construction of discrete Lagrange multipliers and residual functional plays a crucial role in establishing the reliability estimates. The analysis is carried out in a unified setting which holds for a class of discontinuous Galerkin finite element methods. Numerical results are presented to demonstrate the convergence behavior of the error estimator.