{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# These results and those of strouboulis and haque 19

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: een error estimates for odd- and even-order nite element solutions involves a profound, but little known, result of Babuska (cf. 1, 2, 3, 9, 22, 23]). Concentrating on linear second-order elliptic problems on rectangular meshes, Babuska indicates that asymptotically (as mesh spacing tends to zero) errors of odd-degree nite element solutions occur near element edges while errors of even-degree solutions occur in element interiors. These ndings suggest that error estimates may be obtained by neglecting errors in element interiors for odd-degree polynomials and neglecting errors on element boundaries for even-degree polynomials. Thus, for piecewise odd-degree approximations, we could neglect the area integrals on the right-hand sides of (7.4.8) or (7.4.9a) and calculate an error estimate by solving + ; Ae(V E ) =< V (pUn ) + (pUn ) >e 2 ~ 8V 2 S N : (7.4.16a) + ; Ae(V E ) =< V (pUn) ; (pUn) >e 2 ~ 8V 2 S N : (7.4.16b) or For piecewise even-degree approximations, the boundary terms in (7.4.8) or (7.4.9a) can be neglected t...
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