Author:
Zhao Mingyang,Zhou Liangjin
Abstract
AbstractThis 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 $k (k \ge 1)$
k
(
k
≥
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.
Funder
Doctoral launch project of Hanshan Normal University
Publisher
Springer Science and Business Media LLC
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