Journal ArticleDOI
Convergence of Mixed Finite-Element Approximations of a Class of Linear Boundary-Value Problems
J. N. Reddy,J. T. Oden +1 more
- Vol. 2, Iss: 2, pp 83-108
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TLDR
In this paper, convergence and general properties of mixed finite element models of a general class of boundary-value problems of the type Au + ku + f = 0, u belongs to R, and B(u - g) = 0 on boundary (R sup 1), B*(Tu - s) = 1 on boundary(R sup 2) are considered.Abstract:
: Convergence and general properties of mixed finite element models of a general class of boundary-value problems of the type Au + ku + f = 0, u belongs to R, and B(u - g) = 0 on boundary (R sup 1), B*(Tu - s) = 0 on boundary (R sup 2) are considered here where u = u(x) is a function defined on a bounded region R of (E sup n), boundary R is the smooth boundary of R, x is a point in R, A is a linear factorable operator, k is a positive constant, and B and B* are operators describing mixed boundary conditions on boundary R. (Author)read more
Citations
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Book ChapterDOI
A mixed finite element method for 2-nd order elliptic problems
P. A. Raviart,J. M. Thomas +1 more
Journal ArticleDOI
On the equivalence of mode decomposition and mixed finite elements based on the Hellinger—Reissner principle: part I: theory
TL;DR: In this article, a theorem is presented which defines the conditions under which an equivalent mixed finite element based on the Hellinger-Reissner principle exists for a given mode decomposition element.
Journal ArticleDOI
Mixed finite-element approximations of linear boundary-value problems
J. N. Reddy,J. T. Oden +1 more
TL;DR: A theory of mixed finite element/Galerkin approximations of a class of linear boundary value problems of the type T*Tu + ku + / = 0 is presented in this paper, in which appropriate notions of consistency, stability and convergence are derived.
Journal ArticleDOI
Formulation and convergence of a mixed finite element method applied to elastic arches of arbitrary geometry and loading
M. Gellert,M.E. Laursen +1 more
TL;DR: In this article, a sophisticated finite element for elastic arches of arbitrary geometry and loading is developed, based on a mixed variational principle, and convergence of the method is proven and rates of convergence for stresses and displacements are established.
References
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Book
Finite Elements of Nonlinear Continua
TL;DR: The Methode des elements finis reference record was created on 2004-09-07, modified on 2016-08-08 as mentioned in this paper, and was used for the reference record.
Book
Approximation of Elliptic Boundary-Value Problems
TL;DR: In this paper, Young developed finite elements (piecewise polynomial shape functions) with piecewise linear basis functions, leading to a 5-point scheme for the Laplace equation.
Journal ArticleDOI
On Dual Extremum Principles in Applied Mathematics.
B. Noble,M. J. Sewell +1 more
TL;DR: In this paper, a unified account of upper and lower bounding principles involving convexity is given, and they bound an energy-type or cost functional application, including linear and nonlinear programming, networks, optimization, control theory and fluid mechanics.