an encyclopedia of finite element definitions

# Mardal–Tai–Winther

 Abbreviated names MTW Orders $$k=3$$ Reference elements triangle, tetrahedron Polynomial set $$\mathcal{Z}^{(18)}_{k}$$ (triangle) $$\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(19)}_{k}$$ (tetrahedron) ↓ Show polynomial set definitions ↓ DOFs On each facet (triangle): normal integral moments with an order $$1$$ Lagrange space, and tangent integral moments with an order $$0$$ Lagrange space On each facet (tetrahedron): normal integral moments with an order $$1$$ Lagrange space, and integral moments with an order $$1$$ Nédélec (first kind) space Number of DOFs triangle: $$9$$tetrahedron: $$24$$ Mapping contravariant Piola continuity Components normal to facets are continuous Categories Vector-valued elements, H(div) conforming elements

## Implementations

 FIAT FIAT.MardalTaiWinther↓ Show FIAT examples ↓ This implementation is incorrect for this element. Symfem "MTW"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. (legacy) UFL "MTW"↓ Show (legacy) UFL examples ↓

## Examples

 triangleorder 3 (click to view basis functions) tetrahedronorder 3 (click to view basis functions)
• Mardal, Kent-Andre, Tai, Xue-Cheng, and Winther, Ragner. A Robust Finite Element Method for Darcy–Stokes Flow, SIAM Journal on Numerical Analysis 40(5), 1605–1631, 2002. [DOI: 10.1137/S0036142901383910] [BibTeX]
• Tai, Xue-Cheng and Winther, Ragner. A discrete de Rham complex with enhanced smoothness, Calcolo 43, 287–306, 2006. [DOI: 10.1007/s10092-006-0124-6] [BibTeX]

## DefElement stats

 Element added 09 January 2021 Element last updated 16 September 2023