Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CURVED DOMAIN APPROXIMATION IN DIRICHLET'S PROBLEM

  • Lee, Mi-Young (Department of Management Information System Konkuk University) ;
  • Choo, Sang-Mok (School of Mathematics and Physics Ulsan University) ;
  • Chung, Sang-Kwon (Department of Mathematics Education Seoul National University)
  • Published : 2003.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to investigate the piecewise wise polynomial approximation for the curved boundary. We analyze the error of an approximated solution due to this approximation and then compare the approximation errors for the cases of polygonal and piecewise polynomial approximations for the curved boundary. Based on the results of analysis, p-version numerical methods for solving Dirichlet's problems are applied to any smooth curved domain.

Keywords

References

  1. SIAM J. Numer. Anal. v.21 no.6 The approximation theory for the p-version of the finite element method M.R.Dorr https://doi.org/10.1137/0721073
  2. Numer. Methods Partial Differential Equations v.12 Mixed finite element methods for nonlinear elliptic problems: The p-Version M.Lee;F.Milner https://doi.org/10.1002/(SICI)1098-2426(199611)12:6<729::AID-NUM6>3.0.CO;2-U
  3. Comput. Methods Appl. Math. v.89 Mixed finite element methods for nonlinear elliptic problems: The p-Version J.T.Oden;L.Demkowicz
  4. Marth. Comp. v.54 On the stability and convergence of higher order mixed finite element methods for second order elliptic problems M.Suri https://doi.org/10.1090/S0025-5718-1990-0990603-X
  5. Proceedings of the AMS summer institute on partial differential equations at Berkeley The Change in solution due to change in domain G.Strang;A.E.Berger
  6. J. Inst. Math. Appl. v.11 Polygonal domain approximation in Dirichlet's problem V.Thomee https://doi.org/10.1093/imamat/11.1.33