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Finite element exterior calculus is an approach to the design and understanding of finite element discretizations for a wide variety of systems of partial differential equations. This approach brings… (More)

This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we… (More)

- Douglas N. Arnold, Ragnar Winther
- Numerische Mathematik
- 2002

Summary. There have been many efforts, dating back four decades, to develop stable mixed finite elements for the stress-displacement formulation of the plane elasticity system. This requires the… (More)

We consider the solution of the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator I−graddiv.… (More)

- Douglas N. Arnold, Richard S. Falk, Ragnar Winther
- Numerische Mathematik
- 2000

Summary. We consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the Hilbert spaces
${\bf H (div)}$ and… (More)

- Torgeir Rusten, Ragnar Winther
- SIAM J. Matrix Analysis Applications
- 1992

- Douglas N. Arnold, Richard S. Falk, Ragnar Winther
- Math. Comput.
- 2007

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and… (More)

- Kent-André Mardal, Ragnar Winther
- Numerical Lin. Alg. with Applic.
- 2011

This survey paper is based on three talks given by the second author at the London Mathematical Society Durham Symposium on Computational Linear Algebra for Partial Differential Equations in the… (More)

- Kent-André Mardal, Xue-Cheng Tai, Ragnar Winther
- SIAM J. Numerical Analysis
- 2002

Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation… (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 in… (More)