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[00549] On the penalty approach in finite difference methods

  • Session Time & Room : 5C (Aug.25, 13:20-15:00) @E705
  • Type : Contributed Talk
  • Abstract : We introduce a finite difference method with the $H^1$ and $L^2$ penalties to solve the elliptic PDEs over curved complicated domains. The sharp convergence of the penalized solution to the original one is provided. The accuracy in both strategies is almost analogous, provided the penalty parameter $\epsilon$ is $O(h^2)$ in the $H^1$ penalty approach and $O(h^4)$ in the $L^2$ penalty approach. The iterative methods developed for the proposed idea are highly efficient and furnish the theoretical outcomes. Keywords: Finite difference method, Elliptic PDEs, Penalty, Curved domain, Cartesian mesh. References: 1. S. Kale, and D. Pradhan, Error estimates of fictitious domain method with an $H^1$ penalty approach for elliptic problems, Comp. Appl. Math., Vol. 41, (2022), pp. 1-21. 2.B. Maury, Numerical Analysis of a finite element/volume penalty method, SIAM J. Numer Anal., Vol. 47(2), pp. 1126-1148, (2009). 3.N. Saito and G. Zhou, Analysis of the fictitious domain method with an $L^2$-penalty for elliptic problems, Numer. Funct. Anal. Optim. Vol. 36, (2015), pp. 501-527. 4.H. Suito, and H. Kawarada, Numerical simulation of spilled oil by fictitious domain method, Japan J. Indust. Appl. Math., Vol. 21, (2004), pp. 219-236.
  • Classification : 65N85, 65N15
  • Format : Talk at Waseda University
  • Author(s) :
    • DEBASISH PRADHAN (Defence Institute of Advanced Technology, Pune - 411025, India)
    • Swapnil Kale (Defence Institute of Advanced Technology, Pune)