Higher order stable generalized finite element method

DOI10.1007/s00211-014-0609-1zbMath1304.65254OpenAlexW2077435258MaRDI QIDQ740807

Uday Banerjee, Qinghui Zhang, Ivo M. Babuška

Publication date: 9 September 2014

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-014-0609-1

zbMATH Keywords

stabilityconvergenceGalerkin methodgeneralized finite element methodconditioning of discrete systempolynomial enrichment

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (34)

Stable generalized finite element methods (SGFEM) for interfacial crack problems in bi-materials ⋮ 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 ⋮ Assessment of the \textit{flat-top} stable GFEM for free vibration analysis ⋮ A Two-Level Additive Schwarz Domain Decomposition Preconditioner for a Flat-Top Partition of Unity Method ⋮ Numerical analysis of plane stress free vibration in severely distorted mesh by generalized finite element method ⋮ A unified enrichment approach addressing blending and conditioning issues in enriched finite elements ⋮ A stable generalized/extended \(p\)-hierarchical FEM for three-dimensional linear elastic fracture mechanics ⋮ Stable generalized finite element method (SGFEM) for three-dimensional crack problems ⋮ Stable generalized finite element method and associated iterative schemes; application to interface problems ⋮ Improved enrichments and numerical integrations in SGFEM for interface 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 ⋮ A novel application of recovered stresses in stress intensity factors extraction methods for the generalized/extended finite element method ⋮ Improved modal analyses using the novel quadrilateral overlapping elements ⋮ 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 ⋮ Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization ⋮ Stable generalized iso-geometric analysis (SGIGA) for problems with discontinuities and singularities ⋮ On the performance of GFEM with trigonometric enrichment in bidimensional dynamic elastoplastic modelling ⋮ 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 ⋮ The orthonormalized generalized finite element method-OGFEM: efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions ⋮ Higher order stable generalized finite element method for the elliptic eigenvalue and source problems with an interface in 1D ⋮ Enriched finite element methods for Timoshenko beam free vibration analysis ⋮ Robustness in stable generalized finite element methods (SGFEM) applied to Poisson problems with crack 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 ⋮ Strongly stable generalized finite element method: application to interface problems ⋮ A generalized isogeometric analysis of elliptic eigenvalue and source problems with an interface ⋮ Stable generalized finite element method (SGFEM) for parabolic interface problems ⋮ 2-D fracture mechanics problems by SGFEM

Uses Software

• XFEM

Cites Work

• Unnamed Item
• Stable generalized finite element method (SGFEM)
• Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
• Stable enrichment and local preconditioning in the particle-partition of unity method
• A non-conformal extended finite element approach: integral matching Xfem
• An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites
• A multiscale finite element method for elliptic problems in composite materials and porous media
• The partition of unity finite element method: basic theory and applications
• The design and analysis of the generalized finite element method
• Superconvergence in the generalized finite element method
• An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction
• A Particle-Partition of Unity Method--Part II: Efficient Cover Construction and Reliable Integration
• Multiscale XFEM-modelling and simulation of the inelastic material behaviour of textile-reinforced polymers
• Development of a quadratic finite element formulation based on the XFEM and NURBS
• A robust preconditioning technique for the extended finite element method
• A new multiscale finite element method for high-contrast elliptic interface problems
• Interface handling for three-dimensional higher-order XFEM-computations in fluid-structure interaction
• Improved implementation and robustness study of the X-FEM for stress analysis around cracks
• Multiscale Finite Element Methods
• An efficient finite element method for embedded interface problems
• The XFEM for high-gradient solutions in convection-dominated problems
• The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction
• Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
• Elastic crack growth in finite elements with minimal remeshing
• Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
• THE PARTITION OF UNITY METHOD
• Survey of meshless and generalized finite element methods: A unified approach
• Extended finite element method for three-dimensional crack modelling
• A finite element method for crack growth without remeshing
• On the Finite Element Solution of the Pure Neumann Problem
• High-order extended finite element method for cracked domains
• The generalized finite element method

This page was built for publication: Higher order stable generalized finite element method