1. Interpolating Shape Functions
Wednesday, 10/16/2002

2. Local Interpolation (1D)

3. Local Shape Function (1D)

4. 1D Shape Function in Local Coordinate System

5. 1D Shape Function

6. Global Shape Function (1D)

7. Out of Cell Shape Function is 0

8. 2D Shape Function
1D Shape Function

9. 2D Interpolation Surface

10. Interpolation Surface

11. Shape Function (2D)

12. Bilinear Shape Function

13. 2D Shape Function

14. 2D Global Shape Function
L is half of the cell size

15. Out of Cell Shape Function is Zero

16. Properties of Shape Function
(1) Partition of unity
(2) Positive
(3) Kronecker delta
m and n are grid nodes.
(4) Interpolation
(5) Smooth everywhere, except at nodes where they are continuous.