A Nitsche embedded mesh method

DOI10.1007/s00466-011-0641-2zbMath1366.74075OpenAlexW2004219896MaRDI QIDQ432161

Tod A. Laursen, Jessica Sanders, Michael A. Puso

Publication date: 3 July 2012

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://digital.library.unt.edu/ark:/67531/metadc869398/

zbMATH Keywords

interfacesNitsche's methodembedded mesh

Mathematics Subject Classification ID

Structured surfaces and interfaces, coexistent phases (74A50) 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 (47)

Meshless analysis of shear deformable shells: boundary and interface constraints ⋮ A stabilized, symmetric Nitsche method for spatially localized plasticity ⋮ Nitsche method for isogeometric analysis of Reissner-Mindlin plate with non-conforming multi-patches ⋮ Stabilized method of imposing Dirichlet boundary conditions using a recovered stress field ⋮ An ``immersed finite element method based on a locally anisotropic remeshing for the incompressible Stokes problem ⋮ An embedded mesh method for treating overlapping finite element meshes ⋮ The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models ⋮ Modelling interfacial cracking with non-matching cohesive interface elements ⋮ Higher order meshless approximation applied to finite difference and finite element methods in selected thermomechanical problems ⋮ A study on unfitted 1D finite element methods ⋮ A weighted Nitsche stabilized method for small-sliding contact on frictional surfaces ⋮ Mixed-dimensional coupling for time-dependent wave problems using the Nitsche method ⋮ A primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes ⋮ A numerical method for finite-strain mechanochemistry with localised chemical reactions treated using a Nitsche approach ⋮ Parameter-free, weak imposition of Dirichlet boundary conditions and coupling of trimmed and non-conforming patches ⋮ Finite strain primal interface formulation with consistently evolving stabilization ⋮ Modelling complex high speed multimaterial evolutions using a single mesh multivelocity strategy ⋮ A robust Nitsche's formulation for interface problems with spline-based finite elements ⋮ A dual mortar embedded mesh method for internal interface problems with strong discontinuities ⋮ Multipatch isogeometric analysis for geometrically exact shell elements using B-bar method and Bézier extraction ⋮ On the Use of Anisotropic Triangles with Mixed Finite Elements: Application to an “Immersed” Approach for Incompressible Flow Problems ⋮ Adaptive multi-patch isogeometric phase-field method for quasi-static brittle fracture based on Nitsche's method ⋮ An adaptive phase-field simulation for hydrogen embrittlement fracture with multi-patch isogeometric method ⋮ An adaptive multi-patch isogeometric phase-field model for dynamic brittle fracture ⋮ Volumetric embedded entities for the isogeometric analysis of complex structures ⋮ The Nitsche method applied to a class of mixed-dimensional coupling problems ⋮ Numerical procedure to couple shell to solid elements by using Nitsche's method ⋮ Consistent immersed volumetric Nitsche methods for composite analysis ⋮ An embedded mesh method in a multiple material ALE ⋮ A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis ⋮ A variational multiscale discontinuous Galerkin formulation for both implicit and explicit dynamic modeling of interfacial fracture ⋮ Thermoelasticity at finite strains with weak and strong discontinuities ⋮ A stabilized finite element method for enforcing stiff anisotropic cohesive laws using interface elements ⋮ Weak imposition of constraints for structural membranes in transient geometrically nonlinear isogeometric analysis on multipatch surfaces ⋮ A mortar-type finite element approach for embedding 1D beams into 3D solid volumes ⋮ A robust Nitsche's formulation for interface problems ⋮ Coupling finite element method with meshless finite difference method in thermomechanical problems ⋮ Nitsche's method for two and three dimensional NURBS patch coupling ⋮ Primal interface formulation for coupling multiple PDEs: a consistent derivation via the variational multiscale method ⋮ A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. I: Single interface ⋮ An efficient patch-to-patch method for coupling independent finite element subdomains with intersecting interfaces ⋮ Interfacial stabilization at finite strains for weak and strong discontinuities in multi-constituent materials ⋮ Embedded shell finite elements: solid-shell interaction, surface locking, and application to image-based bio-structures ⋮ A Robust Discontinuous Galerkin High-Order Finite Element Method for Elasticity Problems with Interfaces ⋮ A modified perturbed Lagrangian formulation for contact problems ⋮ Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes ⋮ Nitsche's method for Helmholtz problems with embedded interfaces

Cites Work

• Immersed finite element method
• Imposing essential boundary conditions in mesh-free methods
• A formulation for frictionless contact problems using a weak form introduced by Nitsche
• The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuška-Brezzi condition
• A Chimera method based on a Dirichlet/Neumann(Robin) coupling for the Navier--Stokes equations.
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• A fictitious domain method for Dirichlet problem and applications
• On some techniques for approximating boundary conditions in the finite element method
• A comparison of mortar and Nitsche techniques for linear elasticity
• 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)
• An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction
• A fictitious domain/mortar element method for fluid-structure interaction
• Analysis of a Chimera method
• An efficient finite element method for embedded interface problems
• A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
• On methods for stabilizing constraints over enriched interfaces in elasticity
• A discontinuous-Galerkin-based immersed boundary method
• The Finite Element Method with Penalty
• A finite element method for domain decomposition with non-matching grids
• A finite element method for crack growth without remeshing
• The Arlequin method as a flexible engineering design tool

This page was built for publication: A Nitsche embedded mesh method