Unfitted extended finite elements for composite grids

DOI10.1016/j.camwa.2018.05.028zbMath1428.65081OpenAlexW2809040639MaRDI QIDQ2334897

Stefano Zonca, Christian Vergara, Luca Formaggia

Publication date: 8 November 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.05.028

zbMATH Keywords

extended finite element methoddiscontinuous Galerkinunfitted meshes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (6)

Grid-characteristic method using chimera meshes for simulation of elastic waves scattering on geological fractured zones ⋮ An XFEM/DG approach for fluid-structure interaction problems with contact. ⋮ A matrix-free Chimera approach based on Dirichlet-Dirichlet coupling for domain composition purposes ⋮ Multimesh finite elements with flexible mesh sizes ⋮ A multimesh finite element method for the Navier-Stokes equations based on projection methods ⋮ A partition of unity approach to fluid mechanics and fluid-structure interaction

Uses Software

• XFEM
• CutFEM

Cites Work

• Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons
• Ghost penalty
• Mathematical aspects of discontinuous Galerkin methods.
• A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity
• A robust Nitsche's formulation for interface problems
• A stabilized Nitsche overlapping mesh method for the Stokes problem
• A new face-oriented stabilized XFEM approach for 2D and 3D incompressible Navier-Stokes equations
• An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces
• Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures
• Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods
• Analysis of backward Euler/extended finite element discretization of parabolic problems with moving interfaces
• Stabilized explicit coupling for fluid-structure interaction using Nitsche's method
• A finite element method for the simulation of strong and weak discontinuities in solid mechanics
• A cut finite element method for a Stokes interface problem
• A semi-Lagrangean time-integration approach for extended finite element methods
• Equivalent polynomials for quadrature in Heaviside function enriched elements
• CutFEM: Discretizing geometry and partial differential equations
• Optimal convergence analysis for the extended finite element method
• An Unfitted Formulation for the Interaction of an Incompressible Fluid with a Thick Structure via an XFEM/DG Approach
• Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
• A finite element method on composite grids based on Nitsche's method
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Efficient Implementation of Finite Element Methods on Nonmatching and Overlapping Meshes in Three Dimensions

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