HDG methods for the unilateral contact problem

Abstract

Abstract This article presents the HDG approximation as a solution to the unilateral contact problem, leveraging the regularization method and an iterative procedure for resolution. In our study, u represents the potential (displacement of the elastic body) and q represents the flux (the force exerted on the body). Our analysis establishes that the utilization of polynomials of degree k ( k ≥ 1 ) $k (k \ge 1)$ leads to achieving an optimal convergence rate of order k + 1 $k+1$ in L 2 $L^{2}$ -norm for both u and q. Importantly, this optimal convergence is maintained irrespective of whether the domain is discretized through a structured or unstructured grid. The numerical results consistently align with the theoretical findings, underscoring the effectiveness and reliability of the proposed HDG approximation method for unilateral contact problems.

Keywords

• HDG approximation
• Unilateral contact problem
• Regularization method
• Convergence rate