{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

48 or 749a and calculate an error estimate by solving

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: o yield Ae(V E ) = (V f )e ; Ae(V U ) ~ 8V 2 S N : (7.4.17a) 26 Analysis of the Finite Element Method or Ae(V E ) = (V r)e ~ 8V 2 S N : (7.4.17b) Yu 22, 23] used these arguments to prove asymptotic convergence of error estimates to true errors for elliptic problems. Adjerid et al. 2, 3] obtained similar results for transient parabolic systems. Proofs, in both cases, apply to a square region with square p elements of spacing h = 1= N . A typical result follows. 1 N Theorem 7.4.1. Let u 2 HE \ H p+2 and U 2 SE be solutions of (7.4.2) using complete piecewise-bi-polynomial functions of order p. 1. If p is an odd positive integer then ke( )k2 = kE ( )k2 + O(h2p+1 ) 1 1 (7.4.18a) N24 h2 X X X U (P )]2 kE k = 16(2p + 1) e=1 i=1 k=1 xi k e i (7.4.18b) where 2 1 Pk e, k = 1 2 3 4, are the coordinates of the vertices of e, and f (P)]i denotes the jump in f (x) in the direction xi , i = 1 2, at the point P. 2. If p is a positive even integer then (7.4.18a) is satis ed with Ae(Vi E ) = (V f )e ; Ae(Vi U ) (7.4.18c) where E (x1 x2 ) = b1 e Vi(x1 x2 ) =...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern