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  • Session Time & Room : 3E (Aug.23, 17:40-19:20) @E711
  • Type : Contributed Talk
  • Abstract : The obstacle problem, often considered as a prototype for a class of free boundary problems. The elliptic obstacle problem is a nonlinear model that describes the vertical movement of a object restricted to lie above a barrier $\text{(obstacle)}$ while subjected to a vertical force. In this talk, we perform a posteriori error analysis in the supremum norm for the quadratic Discontinuous Galerkin$\text{(DG)}$ method for the elliptic obstacle problem. Compare with the energy norm estimates, supremum norm estimates gives the pointwise control on the error. We have carried out the analysis on two different discrete sets, one set having integral constraints and other one with the nodal constraints at the quadrature points, and discuss the pointwise reliability and efficiency of the proposed a posteriori error estimator. In the analysis, we employ a linear averaging function to transfer DG finite element space to standard conforming finite element space and exploit the sharp bounds on the Green's function of the Poisson's problem. Moreover, the upper and the lower barrier functions corresponding to continuous solution $u$ are constructed by modifying the conforming part of the discrete solution $u_h$ appropriately. Finally, the numerical results for adaptive FEM are presented in order to exhibit the reliability and the efficiency of the proposed error estimator.
  • Classification : 65N30, 65N15
  • Format : Talk at Waseda University
  • Author(s) :
    • Ritesh Ritesh (Indian Institute of Technology, Delhi)
    • Rohit Khandelwal (Indian Institute of Technology, Delhi)
    • Kamana Porwal (Indian Institute of Technology, Delhi)