Approximation of the three-field Stokes system via optimized quadrilateral finite elements

Approximation of the three-field Stokes system via optimized quadrilateral finite elements

— In a recent paper the first two authors showed that a convenient choice of « bubble tensors » leads to a significant réduction of the number of degrees offreedom needed to definefinite element spaces for the extra stresses, suitablefor the solution of viscoelastic flow problems. In this context specialists' usual guiding criterion is a stable and accurate approximation of the underlying linea...

Approximation by quadrilateral finite elements

We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then transformed to a space of functions on each convex quadrilateral element via a bilinear isomorphism of the square onto the element. It is known that for affine...

Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions

New Quadrilateral Mixed Finite Elements

In this paper, we introduce a new family of mixed finite element spaces of higher order (k ≥ 1) on general quadrilateral grids. A typical element has two fewer degrees of freedom than the well-known RaviartThomas finite element RT[k], yet enjoys an optimal-order approximation for the velocity in L 2-norm. The order of approximation in the divergence norm is one less than the velocity, as is com...

Quadrilateral H(div) Finite Elements

We consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the Piola transform, extending results previously obtained for scalar approximation. The finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element, which is then transformed to a space of vector fields on each conve...