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
Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow
TL;DR: In this article, a linearized model of incompressible inviscid flow is considered and a regularisation based on the Hodge Laplacian is used to prove existence and uniqueness of weak solutions for smooth domains.
Finite element modelling of free‐surface flows with non‐hydrostatic pressure and k–ε turbulence model
TL;DR: In this article, a numerical solution based on the unsteady Reynolds-averaged Navier-Stokes equations on the unstructured grid was proposed for free-surface flow.
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A domain-specific language for the hybridization and static condensation of finite element methods
TL;DR: A domain-specific language (DSL) for concisely expressing localized linear algebra on finite element tensors, and its integration within a code-generation framework is introduced.
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Convergence of a $B$-$E$ based finite element method for MHD models on Lipschitz domains
Kaibo Hu,Weifeng Qiu,Ke Shi +2 more
TL;DR: A key estimate for divergence-free finite element functions for a new type of boundary conditions is established and it is rigorously proved the convergence of Picard iterations and the finite element schemes with weak regularity assumptions is proved.
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A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model
TL;DR: In this paper, a stable mixed discontinuous Galerkin (DG) formulation for the double porosity/permeability (DPP) model is proposed, which describes the flow of a single phase incompressible fluid through a porous medium exhibiting two dominant pore-networks with a possibility of mass transfer across them.
12
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.