Generalizations of the finite element method
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Publication:432221
DOI10.2478/s11533-011-0112-1zbMath1245.65159OpenAlexW2093926465MaRDI QIDQ432221
Publication date: 3 July 2012
Published in: Central European Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2478/s11533-011-0112-1
stabilitygeneralized finite element methodpartition of unity methodextended finite element methodmeshfree generalizations
Boundary value problems for second-order elliptic equations (35J25) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical methods for partial differential equations, boundary value problems (65N99)
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Uses Software
Cites Work
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- A note on the conditioning of a class of generalized finite element methods
- Stable generalized finite element method (SGFEM)
- Stable enrichment and local preconditioning in the particle-partition of unity method
- Multilevel particle-partition of unity method
- Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method
- The generalized finite element method for Helmholtz equation. II: Effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment
- Analysis and applications of a generalized finite element method with global-local enrichment functions
- The generalized product partition of unity for the meshless methods
- An extended pressure finite element space for two-phase incompressible flows with surface tension
- The mixed-cell-complex partition-of-unity method
- Multigrid methods for the computation of singular solutions and stress intensity factors. II: Crack singularities
- Meshless methods: An overview and recent developments
- An \(h\)-\(p\) adaptive method using clouds
- The partition of unity finite element method: basic theory and applications
- Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids.
- Multigrid methods for the computation of singular solutions and stress intensity factors. III: Interface singularities.
- Modeling quasi-static crack growth with the extended finite element method. I: Computer implementation
- The method of finite spheres
- A parallel multilevel partition of unity method for elliptic partial differential equations
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- The design and analysis of the generalized finite element method
- On the use of singular functions with finite element approximations
- The generalized finite element method for Helmholtz equation: theory, computation, and open problems
- Multilevel preconditioning for partition of unity methods: some analytic concepts
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities
- Arbitrary discontinuities in finite elements
- Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results
- A Particle-Partition of Unity Method--Part II: Efficient Cover Construction and Reliable Integration
- A partition of unity finite element method for simulating non-linear debonding and matrix failure in thin fibre composites
- Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
- A robust preconditioning technique for the extended finite element method
- A partition of unity finite element method for obtaining elastic properties of continua with embedded thin fibres
- The extended/generalized finite element method: An overview of the method and its applications
- p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems
- Improved implementation and robustness study of the X-FEM for stress analysis around cracks
- A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries
- An Extended Finite Element Method for Two-Phase Fluids
- An Algebraic Treatment of Essential Boundary Conditions in the Particle–Partition of Unity Method
- Generalized finite element enrichment functions for discontinuous gradient fields
- A new fast finite element method for dislocations based on interior discontinuities
- An extended finite element library
- A high-order generalized FEM for through-the-thickness branched cracks
- Fast integration and weight function blending in the extended finite element method
- A Particle-Partition of Unity Method Part VIII: Hierarchical Enrichment
- Classical and enriched finite element formulations for Bloch-periodic boundary conditions
- hp-Generalized FEM and crack surface representation for non-planar 3-D cracks
- Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities
- 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
- Extended finite element method for quasi-brittle fracture
- An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension
- A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
- A Particle-Partition of Unity Method Part VI: A p-robust Multilevel Solver
- Representation of singularities with isoparametric finite elements
- A Particle-Partition of Unity Method--Part III: A Multilevel Solver
- Mesh-independentp-orthotropic enrichment using the generalized finite element method
- A Nonconforming Generalized Finite Element Method for Transmission Problems
- A finite element method for crack growth without remeshing
- High-order extended finite element method for cracked domains
- Multiscale enrichment based on partition of unity
- Dislocations by partition of unity
- A generalized finite element method for the simulation of three-dimensional dynamic crack propagation.
- The generalized finite element method
