an encyclopedia of finite element definitions

# Scott–Vogelius

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 Orders $$1\leqslant k$$ Reference elements triangle, tetrahedron Definition This is a mixed element containing these subelements:order $$k$$ vector Lagrange space order $$k-1$$ Lagrange space Number of DOFs triangle: $$(k+1)(3k+4)/2$$tetrahedron: $$(k+1)(k+2)(4k+9)/6$$ Notes This is the same as the Taylor–Hood element, but the second subelement in this case is discontinuous between cells. Categories Mixed elements

## References

• Scott, L. R. and Vogelius, M. Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 19, 111–143, 1985. [BibTeX]
• Zhang, S. A new family of stable mixed finite elements for the 3D Stokes equations, Mathematics of Computation 74, 543–554, 2005. [DOI: 10.2307/4100078] [BibTeX]