Journal of applied mathematics & informatics

  • 제7권1호
  • /
  • Pages.61-82
  • /
  • 2000
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

$L^{\infty}$-CONVERGENCE OF MIXED FINITE ELEMENT METHOD FOR LAPLACIAN OPERATOR

  • Chen, Huan-Zhen (Department of Mathematics Shandong Normal University) ;
  • Jiang, Zi-Wen (Department of Mathematics Shandong Normal University)
  • 발행 : 2000.01.01

⟨ 이전 논문 다음 논문 ⟩

초록

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

키워드

참고문헌

  1. RAIRO Anal. Numer. v.2 On the existence, uniqueness and approximation of saddle-point problems arising Lagrangian multipliers F. Brezzi
  2. Finite element methods for elliptic problems P. G. Ciarlet
  3. High accuracy theory of finite element methods Chen chuanmiao;Huang yunqing
  4. Math. Comut. v.44 Global estimates for mixed methods for second order elliptic equations J. Douglas, Jr.;J. E. Roberts
  5. Math. Comp. v.51 Sharp maximum norm error estimates for FE approximations of the Stokes problems in 2-D R. Duran;R. H. Nochetto;J. Wang
  6. Bohn Math. Schrift v.89 Eine $L^1$-Fehlerabschatzung fur diskrete Grundlosungen in dermathod der finite element J. Frehse;R. Rannacher
  7. Numer. Math. v.50 Optimal $L^{\infty}$ - estimates for non-conforming and mixed FEM of lowest order L. Gastaldi;R. Nochetto
  8. Elliptic partial differential equation of second order D. Gilberg;N. S. Trudinger
  9. Finite element methods for Navier-Stokes equations V. Girault;P.A. Raviart
  10. RAIRO Anal. Numer. v.15 Error estimates for some mixed finite element methods for parabolic type problems C. Johnson;V. Thomme
  11. Linear and quasilinear equations of elliptic type O. A. Ladyzenskaja;N. N. Ural'ceva
  12. Numer. Math. v.25 Uber die punktweise Konvergent Finiter Elemente F. Natterer
  13. Proc. Conf. on Mathematics Aspects of FEM, Lecture Notes in Math. V. 606 A mixed finite element method for 2nd order elliptic problems P. A. Raviart;J. M. Thomas
  14. Math. Comp. v.38 Some optimal error estimates for piecewise linear finite element approximations R. Rannacher;R. Scott
  15. Calcolo v.20 Optimal $L^{\infty}$- estimates for a mixed FEM for elliptic and parabolic problems R. Scholz
  16. RAIRO Anal. Numer. v.11 $L^{\infty}$-Convergence of saddle-point approximations for second order problems R. Scholz
  17. Math. Comp. v.30 Optimal $L^{\infty}$-estimates for the finite element method on irregular meshes R. Scott
  18. Numer. Math. v.55 Asympotic expansion and $L^{infty}$-error estimates for mixed FEM for second order elliptic problems J. Wang