Strong and weak arbitrary discontinuities in spectral finite elements

By A. Legay, Hongwu Wang, Ted Belytschko. 2005

95 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fd491f9faa21129fb153102e8c00ffadf7973695

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, background): “There are several recent approache s besides the finite cell method that combine higher-order approximations with the fictitious domain idea [93,103,118].”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “With suitable extensions of the algorithm, quadrature schemes can also be developed for higher-order finite elements and weak discontinuities [76–80].”
Studied X-FEM enrichment to handle material interfaces with higher order finite element (2010, background): “In [16], X-FEM is developedwith spectral elements, to deal with arbitrary discontinuities: optimal rate of convergence in energy norm are not reached for curved discontinuities, and integration is more delicate.”
Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods (2008, background): “The larger approximation space of higher-order spectral elements has also been shown to improve the accuracy in the blending elements [11].”
Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes (2011, background): “…a discontinuous formulation, one can either turn to a discontinuous version of the SEM (Bernardi et al. 1994; Chaljub 2000; Kopriva et al. 2002; Chaljub et al. 2003; Legay et al. 2005; Kopriva 2006; Wilcox et al. 2010; Acosta Minolia & Kopriva 2011) or to a discontinuous Galerkin technique.”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “For example, the shape functions of hierarchical FEs [126], spectral FEs [113], or higher-order Lagrange elements [175, 45] have been applied.”
Higher‐order XFEM for curved strong and weak discontinuities (2009, methodology): “Curved interfaces are discussed in [22, 23] where for integration purposes the curvature is neglected, and in [17] where a quadrature for curved interfaces is proposed.”
Enhanced blending elements for XFEM applied to linear elastic fracture mechanics (2009, methodology): “[25] use the XFEM concept within spectral FEs for modelling discontinuities in the gradients.”
Enriched finite elements and level sets for damage tolerance assessment of complex structures (2006, methodology): “The method naturally extends to higher order shape functions [31,32].”