Finite Elements

By M. Hoit, G. Consolazio. Handbook of Dynamic System Modeling, 2007

791 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering

View Paper: https://www.semanticscholar.org/paper/8b89bcb34444cc97dab550b92ac14c384442b4fd

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In Civil and Structural Engineering

Citations in the corpus

Some Preconditioning Techniques for Saddle Point Problems (2008, background): “Other examples are provided by mixed finite elements for incompressible flow problems, when some form of pressure stabilization is included in the discretization [13], and by the modeling of slightly compressible material in linear elasticity theory [7].”
Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems (2016, methodology): “With the conformity of the methods, the continuity and coercivity of the continuous problems are inherited by the discrete methods implying error estimates which can be proved in a standard way by imitating the steps for proving Cea’s lemma [39]:”
A positive and bounded finite element approximation of the generalized Burgers–Huxley equation (2015, positive): “From the theory of finite element interpolation [3, 5], we have that for Ih, the interpolant of the exact solution u in the space of piecewise linear continuous polynomials, and Λ = u − Ihu, there exist a constant C ≥ 0 such that ‖Λ‖+ h‖∇Λ‖ ≤ Ch(2)‖u‖H2(Ω).”
Convergence of multipoint flux approximations on quadrilateral grids (2006, background): “4), is a standard estimate, and can for instance be found in [10].”
Theory of adaptive finite element methods: An introduction (2009, methodology): “For a hierarchy of quasi-uniform meshes, V-cycle multigrid and BPX-preconditioned conjugate gradient methods can approximate the Ritz-Galerkin solution U of our model problem (13) to a desired accuracy with a number of operations proportional to #T [15, 16].”
Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates (2017, methodology): “The boundary of the plate can be assumed to be piecewise smooth (satisfying the so-called cone condition providing positive interior angles for all vertices [61,62]).”
A unified formulation of small-strain corotational finite elements: I. Theory (2005, methodology): “In the introduction of a key contribution, Nour-Omid and Rankin [54] attribute the original concept of corotational procedures in FEM to Wempner [86] and Belytschko and Hsieh [7].”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, background): “They have long been known as useful C1-nonconforming elements (Braess, 2007; Ciarlet, 2002).”
Neurobiology of Aging: Contents (2005, neutral): “• Computational fluid dynamics [213, 407, 459, 469, 499] • Constrained and weighted least squares estimation [59, 222] • Constrained optimization [210, 506, 507] • Economics [18, 143, 320, 456] • Electrical circuits and networks [51, 109, 449, 467] • Electromagnetism [67, 390, 392] • Finance [348, 3”
New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces (2008, neutral): “Due to the important applications of the original Kantorovich inequality for matrices [25] in statistics [26,40,27,36,43,39,46,35,44,28] and numerical analysis [19,20,37,1,18], any new inequality of this type will have a flow of consequences into other areas.”
A posteriori estimates for the Stokes eigenvalue problem (2009, methodology): “[5]) that the bilinear form B is stable, i.”