Robustness in stable generalized finite element methods (SGFEM) applied to Poisson problems with crack singularities

DOI10.1016/j.cma.2016.08.019zbMath1439.74479OpenAlexW2508376483MaRDI QIDQ2308675

Qinghui Zhang, Uday Banerjee, Ivo M. Babuška

Publication date: 3 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2016.08.019

zbMATH Keywords

convergence analysisrobustnesscondition numberextended FEMgeneralized FEMSGFEM

Mathematics Subject Classification ID

Brittle fracture (74R10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (30)

Stable generalized finite element methods (SGFEM) for interfacial crack problems in bi-materials ⋮ A recycling preconditioning method with auxiliary tip subspace for elastic crack propagation simulation using XFEM ⋮ Well-conditioned and optimally convergent second-order generalized/extended FEM formulations for linear elastic fracture mechanics ⋮ A generalized finite element method without extra degrees of freedom for large deformation analysis of three-dimensional elastic and elastoplastic solids ⋮ A unified enrichment approach addressing blending and conditioning issues in enriched finite elements ⋮ Extended finite element method in mixed-hybrid model of singular groundwater flow ⋮ A stable generalized/extended \(p\)-hierarchical FEM for three-dimensional linear elastic fracture mechanics ⋮ A condensed generalized finite element method (CGFEM) for interface problems ⋮ Stable generalized finite element method (SGFEM) for three-dimensional crack problems ⋮ Condensed generalized finite element method ⋮ Recovery strategies, a posteriori error estimation, and local error indication for second‐order G/XFEM and FEM ⋮ DOF‐gathering stable generalized finite element methods for crack problems ⋮ An extended finite element method with polygonal enrichment shape functions for crack propagation and stiff interfaceproblems ⋮ Extended isogeometric analysis of a progressively fracturing fluid‐saturated porous medium ⋮ A novel application of recovered stresses in stress intensity factors extraction methods for the generalized/extended finite element method ⋮ Sixth-order finite difference scheme for the Helmholtz equation with inhomogeneous Robin boundary condition ⋮ A high-order generalized finite element method for multiscale structural dynamics and wave propagation ⋮ Strongly stable generalized finite element method (SSGFEM) for a non-smooth interface problem ⋮ A stable generalized/extended FEM with discontinuous interpolants for fracture mechanics ⋮ Stable generalized iso-geometric analysis (SGIGA) for problems with discontinuities and singularities ⋮ A stable discontinuity-enriched finite element method for 3-D problems containing weak and strong discontinuities ⋮ Effective Two-Level Domain Decomposition Preconditioners for Elastic Crack Problems Modeled by Extended Finite Element Method ⋮ A simple, first-order, well-conditioned, and optimally convergent generalized/extended FEM for two- and three-dimensional linear elastic fracture mechanics ⋮ Orthogonalized generalized iso-geometric analysis (OGIGA) and its applications to problems of fracture mechanics ⋮ Stable generalized/extended finite element method with global-local enrichment for material nonlinear analysis ⋮ Intrinsic extended isogeometric analysis with emphasis on capturing high gradients or singularities ⋮ A stable generalized finite element method (SGFEM) of degree two for interface problems ⋮ Strongly stable generalized finite element method (SSGFEM) for a non-smooth interface problem. II: A simplified algorithm ⋮ Stable generalized finite element method (SGFEM) for parabolic interface problems ⋮ 2-D fracture mechanics problems by SGFEM

Uses Software

• XFEM

Cites Work

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