Quadratic Discontinuous Galerkin methods for Unilateral Contact Problem

2024/01/04 by Kamana Porwal, Tanvi Wadhawan, Porwal, Kamana +1
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2401.02120

openalex publication_date 2024/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we employ discontinuous Galerkin (DG) methods for the finite element approximation of the frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We first establish an optimal a priori error estimates under the appropriate regularity assumption on the exact solution \bu. Further, we analyze a posteriori error estimates in the DG norm wherein, the reliability and efficiency of the proposed a posteriori error estimator is addressed. The suitable construction of discrete Lagrange multiplier \bλ_h and some intermediate operators play a key role in developing a posteriori error analysis. Numerical results presented on uniform and adaptive meshes illustrate and confirm the theoretical findings.

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