The Mathematica Journal
Volume 9, Issue 3

Search

In This Issue
Articles
Tricks of the Trade
In and Out
Trott's Corner
New Products
New Publications
Calendar
News Bulletins
New Resources
Letters
Classifieds

Download This Issue 

About the Journal
Editorial Policy
Staff and Contributors
Submissions
Subscriptions
Advertising
Back Issues
Contact Information

Algebraic Construction of Smooth Interpolants on Polygonal Domains
Elisabeth Anna Malsch
Gautam Dasgupta

Enforcing Global Linearity

If some of the interpolating functions do not satisfy the same linearity conditions that the convex shape functions satisfy, they can be altered. Given the entire set of interpolating functions corresponding to the nodal points and the set of functions that correspond to the points on the convex hull, the following requirement can be imposed:

When the function is either 1, , or , the convex interpolant satisfies the requirement exactly over the convex hull points:

The functions can be modified to ensure linearity:

When the points are not the convex hull points and , boundedness is not necessarily preserved.

For example, construct linearized interpolations on a quadrilateral.

Figure 10. Linearized interpolants.



     
About Mathematica | Download Mathematica Player
© Wolfram Media, Inc. All rights reserved.