{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 38a 16 analysis of the finite element method where

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n @ ~ . (Thus, S0 is not a subspace of H01.) Figure 7.3.1: Approximation of a curved boundary by a polygon. For piecewise linear polynomial approximations on triangles they show that ku ; U k1 = O(h) and for piecewise quadratic approximations ku ; U k1 = O(h3=2). The poor accuracy with quadratic polynomials is due to large errors in a narrow \boundary layer" near @ . Large errors are con ned to the boundary layer and results are acceptable elsewhere. Wait and Mitchell 21], Chapter 6, quote other results which prove that ku ; U k1 = O(hp) for pth degree piecewise polynomial approximations when the distance between @ and @ ~ is O(hp+1). Such is the case when @ is approximated by p th degree piecewise-polynomial interpolation. 7.4 A Posteriori Error Estimation In previous sections of this chapter, we considered a priori error estimates. Thus, we can, without computation, infer that nite element solutions converge at a certain rate depending on the exact solution's smoothness. Error bounds are expressed in terms of unknown constants which are di cult, i...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online