Higher‐order XFEM for curved strong and weak discontinuities

By K. Cheng, Thomas-Peter Fries. 2009

217 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3ac830d673b9a0f2ef477d062b3bd5f5083c7609

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

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.”
An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies (2013, methodology): “This issue has already been addressed in applications to weak discontinuities and a number of techniques have been developed to overcome the drawback caused by the blending elements [30–36].”
X‐FEM in isogeometric analysis for linear fracture mechanics (2011, background): “For higher order basis functions, a linear Ñ may be preferred [21, 22].”
A robust Nitsche's formulation for interface problems with spline‐based finite elements (2015, background): “Cheng and Fries [4] used a higher-order representation of the level set to describe the interface with higher-order accuracy.”
Dual-horizon peridynamics: A stable solution to varying horizons (2017, background): “Meanwhile, PD can be easily extended from 2D to 3D, which cannot always be done in other methods [4–6].”
Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “Concerning the accurate integration on the cut cells, other approaches such as the estimation of the discontinuous integrands with the continuous functions [35–37], or local mesh generation are also applicable [38–40].”