A stable extended/generalized finite element method with Lagrange multipliers and explicit damage update for distributed cracking in cohesive materials

Csati, Zoltan; Moës, Nicolas; Massart, Thierry

doi:10.1016/j.cma.2020.113173

Cited by 6 publications

(1 citation statement)

References 40 publications

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“…The accuracy of the finite element method is increased by a selection of the basis and a suitable mesh refinement. Lagrange [13,14], Bernstein [15], Hermite [16], Argyris [17], and radial basis functions [18] are some classical bases that can be used to construct finite dimensional function spaces. In addition, it has been demonstrated in numerous studies that the finite element method based on spline basis functions is applied to many differential equations, and high precision has been obtained.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Second-Order Elliptic Equations with C-Bézier Basis

Sun,

Su,

Pang

2024

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This article introduces a finite element method based on the C-Bézier basis function for second-order elliptic equations. The trial function of the finite element method is set up using a combination of C-Bézier tensor product bases. One advantage of the C-Bézier basis is that it has a free shape parameter, which makes geometric modeling more convenience and flexible. The performance of the C-Bézier basis is searched for by studying three test examples. The numerical results demonstrate that this method is able to provide more accurate numerical approximations than the classical Lagrange basis.

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