A new partition of unity finite element free from the linear dependence problem and possessing the delta property

106 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Modeling bimaterial interface cracks using the numerical manifold method (2013, methodology): “In literature, some methods [33–35] have been proposed to alleviate the linear dependence problem in PUFEMs.”
New strategies for some issues of numerical manifold method in simulation of crack propagation (2014, background): “[8] suggested a configuration of DOFs free from the rank dependency issue, where the patches of inner nodes are assigned to incomplete quadratic polynomials excluding monomials of x(2) and y(2), while the”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “Extrinsic enrichment can lead to an ill-conditioned global stiffness matrix [28] as is the case with many other PU methods, due to the additional unknowns at nodes that do not correspond to the physical degrees of freedom [29].”
Phase-field modeling of fracture in linear thin shells (2014, unknown): “The Dirichlet displacement and rotation boundary conditions are imposed with Lagrange multipliers, the interested reader is referred to [48, 49, 38, 50].”