Journal ArticleDOI
A family of mixed finite elements for linear elasticity
TLDR
In this paper, a family of finite elements for use in mixed formulations of linear elasticity is developed, where the stresses are not required to be symmetric, but only to satisfy a weaker condition based upon Lagrange multipliers.Abstract:
A family of finite elements for use in mixed formulations of linear elasticity is developed. The stresses are not required to be symmetric, but only to satisfy a weaker condition based upon Lagrange multipliers. This is based on the same formulation used in the PEERS finite element spaces. Elements for both two and three dimensional problems are given. Error analysis on these elements is done, and some superconvergence results are proved.read more
Citations
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Journal ArticleDOI
Finite element exterior calculus, homological techniques, and applications
TL;DR: Finite element exterior calculus as mentioned in this paper is an approach to the design and understand- ing of finite element discretizations for a wide variety of systems of partial differential equations, which brings to bear tools from differential geometry, algebraic topology, and homological algebra to develop discretiza- tions which are compatible with the geometric, topological and algebraic structures which underlie well-posedness of the PDE problem being solved.
Journal ArticleDOI
Mixed finite element methods for linear elasticity with weakly imposed symmetry
TL;DR: New finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima- tions to both stresses and displacements are constructed.
Journal ArticleDOI
Nonconforming finite element methods for the equations of linear elasticity
TL;DR: In this article, an appropriate discrete version of Korn's second inequality is shown to hold for piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears.
Journal ArticleDOI
A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging
TL;DR: In this paper, a review of the spectral and finite-difference methods for geophysical interpretation is carried out, focusing on the spectral method, which is very efficient and accurate but generally restricted to simple earth structures and often layered earth structures.
Journal ArticleDOI
Reduced symmetry elements in linear elasticity
TL;DR: In this article, the authors present two ways of introducing elements with reduced symmetry, one based on Stokes problems, and the other based on the nice property of several interpolation operators, which allows to prove the convergence of the Arnold-Falk-Winther element with simple and standard arguments, without the use of the============Berstein-Gelfand Gelfand resolution.
References
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Book
Navier-Stokes Equations
TL;DR: Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.
Journal ArticleDOI
Mixed finite elements in ℝ 3
TL;DR: In this article, the authors present two families of non-conforming finite elements, built on tetrahedrons or on cubes, which are respectively conforming in the spacesH(curl) and H(div).
Journal ArticleDOI
On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers
TL;DR: In this paper, the authors describe a fitting for hose end fittings that is suitable for use in conjunction with a cross-linked polyethylene hose or pipe, where a body incorporating a nipple adapted for insertion in a pipe end and a clamping ring normally retained on the body and adapted for clamping action about the outer surface of said pipe end is described.
Journal ArticleDOI
Approximation by finite element functions using local regularization
TL;DR: In this paper, the authors give an elementary proof of a theorem of approximation of Sobolev spaces by fimte éléments without to use classical interpolation, which allows us in some cases to fit boundary conditions.
Journal ArticleDOI
Two families of mixed finite elements for second order elliptic problems
TL;DR: In this article, two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces.