The high-order shifted boundary method and its analysis
From MaRDI portal
Publication:2136721
DOI10.1016/j.cma.2022.114885OpenAlexW4225854141MaRDI QIDQ2136721
Guglielmo Scovazzi, Claudio Canuto, Nabil M. Atallah
Publication date: 12 May 2022
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.2022.114885
immersed boundary methodhigh-order methodunfitted finite element methodsapproximate domain boundariessmall cut-cell problemshifted boundary method
Error bounds for boundary value problems involving PDEs (65N15) 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)
Related Items
The simple shifted fracture method ⋮ A quasi-conforming embedded reproducing kernel particle method for heterogeneous materials ⋮ High-order enforcement of jumps conditions between compressible viscous phases: an extended interior penalty discontinuous Galerkin method for sharp interface simulation ⋮ An enriched shifted boundary method to account for moving fronts ⋮ Complex-geometry simulations of transient thermoelasticity with the shifted boundary method ⋮ Optimal surrogate boundary selection and scalability studies for the shifted boundary method on octree meshes ⋮ A penalty-free shifted boundary method of arbitrary order ⋮ eXtended hybridizable discontinuous Galerkin (X-HDG) method for linear convection-diffusion equations on unfitted domains ⋮ A shifted boundary method based on extension operators ⋮ Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer ⋮ Shifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes ⋮ Robust high-order unfitted finite elements by interpolation-based discrete extension
Uses Software
Cites Work
- An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
- Numerical integration over implicitly defined domains for higher order unfitted finite element methods
- Subdivision-stabilised immersed b-spline finite elements for moving boundary flows
- Ghost penalty
- Boundary-conforming discontinuous Galerkin methods via extensions from subdomains
- Isogeometric analysis using T-splines
- The shifted boundary method for hyperbolic systems: embedded domain computations of linear waves and shallow water flows
- The finite cell method for three-dimensional problems of solid mechanics
- Isogeometric analysis of structural vibrations
- Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
- A new finite element formulation for computational fluid dynamics. VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
- What are \(C\) and \(h\)?: Inequalities for the analysis and design of finite element methods
- On the constants in \(hp\)-finite element trace inverse inequalities.
- Fictitious domain method with boundary value correction using penalty-free Nitsche method
- A new face-oriented stabilized XFEM approach for 2D and 3D incompressible Navier-Stokes equations
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow
- Analysis of the shifted boundary method for the Stokes problem
- A high order mixed-FEM for diffusion problems on curved domains
- The shifted boundary method for embedded domain computations. I: Poisson and Stokes problems
- The shifted boundary method for embedded domain computations. II: Linear advection-diffusion and incompressible Navier-Stokes equations
- A cut finite element method with boundary value correction for the incompressible Stokes equations
- The second-generation shifted boundary method and its numerical analysis
- A priori and a posteriori error analyses of a high order unfitted mixed-FEM for Stokes flow
- An optimally convergent higher-order finite element coupling method for interface and domain decomposition problems
- Dirichlet boundary value correction using Lagrange multipliers
- Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines
- High order unfitted finite element methods on level set domains using isoparametric mappings
- 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)
- Flow patterns around heart valves: A numerical method
- Cut finite element methods for linear elasticity problems
- Analysis of a Method to Parameterize Planar Curves Immersed In Triangulations
- A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity
- Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains
- Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes
- CutFEM: Discretizing geometry and partial differential equations
- A face-oriented stabilized Nitsche-type extended variational multiscale method for incompressible two-phase flow
- Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems
- An unfitted finite element method using discontinuous Galerkin
- A Robust Finite Element Method for Nonhomogeneous Dirichlet Problems in Domains with Curved Boundaries
- Analysis of a high-order unfitted finite element method for elliptic interface problems
- A cut finite element method with boundary value correction
- Projection Methods for Dirichlet's Problem in Approximating Polygonal Domains with Boundary-Value Corrections
- Finite Element Methods with B-Splines
- A finite element method for crack growth without remeshing
- A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries
- Analysis of the shifted boundary method for the Poisson problem in domains with corners
- A posteriori error estimates with boundary correction for a cut finite element method
- Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
- An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems
- Unnamed Item
