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- Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, L. Donatella Marini
- SIAM J. Numerical Analysis
- 2002

We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuousâ€¦ (More)

- ANALYSE NUMÃ‰RIQUE, Douglas N. Arnold, Franco Brezzi
- 2009

We discuss a technique of implementing certain mixed f mite Ã©lÃ©ments based on the use of Lagrange multipliers to impose interelement continuity The matrices ansingfrom this implementation areâ€¦ (More)

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 bringsâ€¦ (More)

We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubbleâ€¦ (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 weâ€¦ (More)

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

There have been many efforts, dating back four decades, to develop stablemixed finite elements for the stress-displacement formulation of the plane elasticity system. This requires the development ofâ€¦ (More)

Summarizing the work of [AFW97], we show how to construct preconditioners using domain decomposition and multigrid techniques for the system of linear algebraic equations which arises from the finiteâ€¦ (More)

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

We consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the Hilbert spacesH(div) andH(curl) in threeâ€¦ (More)

- Douglas N. Arnold, Daniele Boffi, Richard S. Falk
- Math. Comput.
- 2002

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 aâ€¦ (More)

- Douglas N. Arnold, Franco Brezzi
- Math. Comput.
- 1997

We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and theâ€¦ (More)