an encyclopedia of finite element definitions

# Bogner–Fox–Schmitt

 Orders $$k=3$$ Reference elements quadrilateral Polynomial set $$\mathcal{Q}_{k}$$↓ Show polynomial set definitions ↓ DOFs On each vertex: point evaluations,point evaluations of derivatives in coordinate directions, and point evaluation of mixed second derivative Number of DOFs quadrilateral: $$16$$ Mapping identity continuity Function values and derivatives are continuous. Categories Scalar-valued elements

## Implementations

 Symfem "BFS"↓ Show Symfem examples ↓

## Examples

 quadrilateralorder 3 (click to view basis functions)

## References

• Bogner, F. K., Fox, R. L., and Schmit, L. A. The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulae, Proceedings of the Conference on Matrix Methods in Structural Mechanics, 397–444, 1965. [BibTeX]

## DefElement stats

 Element added 06 March 2021 Element last updated 02 August 2022