Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

APPROXIMATION THEORY FOR THE P-VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS PART II: CONVERGENCE OF THE P VERSION OF THE FINITE ELEMENT METHOD

BENQI GUO
SIAM Journal on Numerical Analysis
Vol. 47, No. 4 (2009), pp. 2578-2611
Stable URL: http://www.jstor.org/stable/27862746
Page Count: 34
  • Subscribe ($19.50)
  • Cite this Item
APPROXIMATION THEORY FOR THE P-VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS PART II: CONVERGENCE OF THE P VERSION OF THE FINITE ELEMENT METHOD
Preview not available

Abstract

This paper is the second in a series devoted to the approximation theory of the p-version of the finite element method in three dimensions. In this paper, we analyze the approximability of functions in the framework of the Jacobi-weighted Besov and Sobolev spaces in the three-dimensional setting and approximation error of the p-version of the finite element method on meshes containing tetrahedral, hexahedral, and prism elements for elliptic problems with homogeneous and nonhomogeneous Dirichlet boundary condition. The convergence rate is rigorously proved for solutions in H k (Ω). The optimal convergence of the p-version for elliptic problems on polyhedral domains will be analyzed in the forthcoming Part III [B.Q. Guo, Approximation theory of the p-version of the finite element method in three dimensions, Part III: Optimal convergence for problems on polyhedral domains, in preparation] of the series.

Page Thumbnails

  • Thumbnail: Page 
2578
    2578
  • Thumbnail: Page 
2579
    2579
  • Thumbnail: Page 
2580
    2580
  • Thumbnail: Page 
2581
    2581
  • Thumbnail: Page 
2582
    2582
  • Thumbnail: Page 
2583
    2583
  • Thumbnail: Page 
2584
    2584
  • Thumbnail: Page 
2585
    2585
  • Thumbnail: Page 
2586
    2586
  • Thumbnail: Page 
2587
    2587
  • Thumbnail: Page 
2588
    2588
  • Thumbnail: Page 
2589
    2589
  • Thumbnail: Page 
2590
    2590
  • Thumbnail: Page 
2591
    2591
  • Thumbnail: Page 
2592
    2592
  • Thumbnail: Page 
2593
    2593
  • Thumbnail: Page 
2594
    2594
  • Thumbnail: Page 
2595
    2595
  • Thumbnail: Page 
2596
    2596
  • Thumbnail: Page 
2597
    2597
  • Thumbnail: Page 
2598
    2598
  • Thumbnail: Page 
2599
    2599
  • Thumbnail: Page 
2600
    2600
  • Thumbnail: Page 
2601
    2601
  • Thumbnail: Page 
2602
    2602
  • Thumbnail: Page 
2603
    2603
  • Thumbnail: Page 
2604
    2604
  • Thumbnail: Page 
2605
    2605
  • Thumbnail: Page 
2606
    2606
  • Thumbnail: Page 
2607
    2607
  • Thumbnail: Page 
2608
    2608
  • Thumbnail: Page 
2609
    2609
  • Thumbnail: Page 
2610
    2610
  • Thumbnail: Page 
2611
    2611