2014/04/11 by Thirupathi Gudi, Gudi, Thirupathi, Kamana Porwal +1
Computer Science · Engineering · #65N30 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1404.3147
openalex publication_date 2014/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A residual based em a posteriori error estimator is derived for a\nquadratic finite element method (fem) for the elliptic obstacle problem. The\nerror estimator involves various residuals consisting the data of the problem,\ndiscrete solution and a Lagrange multiplier related to the obstacle constraint.\n em A priori error estimates for the Lagrange multiplier have been derived\nand further under an assumption that the contact set does not degenerate to a\ncurve in any part of the domain, optimal order em a priori error estimates\nhave been derived whenever the data and the solution are sufficiently regular,\nprecisely, under the sufficient conditions required for quadratic fem in the\ncase of linear elliptic problem. The numerical experiments of adaptive fem for\na model problem satisfying the above condition on contact set show optimal\norder convergence. This demonstrates that the quadratic fem for obstacle\nproblem can exhibit optimal performance.\n