Book Chapter10.1007/BFB0064470
A mixed finite element method for 2-nd order elliptic problems
P. A. Raviart,J. M. Thomas +1 more
- 01 Jan 1977
- pp 292-315
2.2K
About: The article was published on 01 Jan 1977. The article focuses on the topics: Mixed finite element method & Extended finite element method.
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Citations
A New Superconvergence for Mixed Finite Element Approximations
TL;DR: A new superconvergence result is established for numerical solutions of elliptic problems obtained from the mixed finite element method of Raviart--Thomas over rectangular partitions with improved accuracy of order ${\cal O}(h^{k+3})$ and an appropriately defined local projection of the flux variable when k>0.
13
A multipoint stress mixed finite element method for elasticity on quadrilateral grids
Ilona Ambartsumyan,Ilona Ambartsumyan,Eldar Khattatov,Eldar Khattatov,Jan Martin Nordbotten,Ivan Yotov +5 more
TL;DR: In this article, the authors developed a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive definite cell centered system.
13
On the Construction of Well-Conditioned Hierarchical Bases for (div)-Conforming ℝn Simplicial Elements
Jianguo Xin,Wei Cai,Nailong Guo +2 more
TL;DR: Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedralelements are constructed with the goal of improving the conditioning of the mass and stiffness matrices, and the basis with the triangular element is found to be acceptable up to the approximation of order four.
13
Time Domain Integral Equation Methods in Computational Electromagnetism
Jielin Li,Peter Monk,Daniel S. Weile +2 more
- 01 Jan 2015
TL;DR: This chapter discusses both theoretical and numerical aspects of one approach that solves the stability problem: convolution quadrature, which starts with scattering from a perfectly conducting object and develops the electric field integral equation.
13
Domain Decomposition for a Mixed Finite Element Method in Three Dimensions
TL;DR: The solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions is considered.
References
On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers
Franco Brezzi
- 01 Jan 1974
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.
Primal hybrid finite element methods for 2nd order elliptic equations
P.-A. Raviart,J. M. Thomas +1 more
TL;DR: In this article, the construction of finite element methods for 2nd order elliptic equations based on a primal hybrid variational principle was studied and the optimal error bounds were proved, as well as a general analysis of nonconforming finite element method.
A Mixed Finite Element Method for the Biharmonic Equation
Philippe G. Ciarlet,P.-A. Raviart +1 more
- 01 Jan 1974
TL;DR: In this article, a mixed finite element method for the Biharmonic equation is described, in which the approximate solution lies in a finite-dimensional space and the Laplacian Δu of the solution plays a special role.
247
Dual analysis for heat conduction problems by finite elements
TL;DR: In this paper, an alternative approach to the usual finite element treatment of temperature problems is presented, using approximations for the field of the dual variables, and the appropriate extremum principle is established and its minimization is discussed in connection with a plane triangular finite element process.