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- Douglas N. Arnold, Gerard Awanou
- Foundations of Computational Mathematics
- 2011

We give a new, simple, dimension-independent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s âˆ’ r of the variablesâ€¦ (More)

Multivariate spline functions are smooth piecewise polynomial functions over triangulations consisting of n-simplices in the Euclidean space IR. A straightforward method for using these splineâ€¦ (More)

- Douglas N. Arnold, Gerard Awanou, Ragnar Winther
- Math. Comput.
- 2008

We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field inâ€¦ (More)

- Douglas N. Arnold, Gerard Awanou
- Math. Comput.
- 2014

We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees.â€¦ (More)

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation togetherâ€¦ (More)

- Douglas N. Arnold, Gerard Awanou, Weifeng Qiu
- Adv. Comput. Math.
- 2015

We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, theâ€¦ (More)

We present a family of stable rectangular mixed finite elements for plane elasticity. Each member of the family consists of a space of piecewise polynomials discretizing the space of symmetric tensorâ€¦ (More)

- Gerard Awanou, Ming-Jun Lai
- Math. Comput.
- 2005

We present numerical approximations of the 3D steady state Navier-Stokes equations in velocity-pressure formulation using trivariate splines of arbitrary degree d and arbitrary smoothness r with r <â€¦ (More)

- Gerard Awanou
- Adv. Comput. Math.
- 2015

We present two numerical methods for the fully nonlinear elliptic MongeAmpÃ¨re equation. The first is a pseudo transient continuation method and the second is a pure pseudo time marching method. Theâ€¦ (More)

We discuss the implementation of a C quintic superspline method for interpolating scattered data in IR based on a modification of Alfeldâ€™s generalization of the Clough-Tocher scheme described by Laiâ€¦ (More)