A shifted boundary method based on extension operators

DOI10.1016/j.cma.2024.116782OpenAlexW4390937747WikidataQ129755376 ScholiaQ129755376MaRDI QIDQ6202968

Antonio Rodríguez-Ferran, Claudio Canuto, Guglielmo Scovazzi, Rubén Zorrilla, Riccardo Rossi

Publication date: 26 March 2024

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.2024.116782

zbMATH Keywords

immersed boundary methodunfitted finite element methodsweak boundary conditionsapproximate domain boundariessmall cut-cell problemshifted boundary method

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

• A new fictitious domain method: optimal convergence without cut elements
• Fictitious domain finite element methods using cut elements. II: A stabilized Nitsche method
• Subdivision-stabilised immersed b-spline finite elements for moving boundary flows
• Analysis of the fully discrete fat boundary method
• Ghost penalty
• Boundary-conforming discontinuous Galerkin methods via extensions from subdomains
• Fictitious domain finite element methods using cut elements. I: A stabilized Lagrange multiplier method
• A finite element method for interface problems in domains with smooth boundaries and interfaces
• The shifted boundary method for hyperbolic systems: embedded domain computations of linear waves and shallow water flows
• A Nitsche-based cut finite element method for a fluid-structure interaction problem
• The finite cell method for three-dimensional problems of solid mechanics
• Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
• Generalizing the finite element method: Diffuse approximation and diffuse elements
• The tetrahedral finite cell method for fluids: immersogeometric analysis of turbulent flow around complex geometries
• 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.
• Theory and practice of finite elements.
• A fictitious domain method for Dirichlet problem and applications
• The aggregated unfitted finite element method for elliptic problems
• A modified finite element formulation for the imposition of the slip boundary condition over embedded volumeless geometries
• Analysis of the shifted boundary method for the Stokes problem
• 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 weighted shifted boundary method for free surface flow problems
• The high-order shifted boundary method and its analysis
• CutFEM without cutting the mesh cells: a new way to impose Dirichlet and Neumann boundary conditions on unfitted meshes
• Shape optimization using the cut finite element method
• Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines
• A stabilized mixed discontinuous Galerkin method for Darcy flow
• 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)
• CutFEM based on extended finite element spaces
• Weighted Extended B-Spline Approximation of Dirichlet Problems
• 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
• CutFEM: Discretizing geometry and partial differential equations
• A face-oriented stabilized Nitsche-type extended variational multiscale method for incompressible two-phase flow
• A Robust Finite Element Method for Nonhomogeneous Dirichlet Problems in Domains with Curved Boundaries
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A cut finite element method with boundary value correction
• The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments
• Projection Methods for Dirichlet's Problem in Approximating Polygonal Domains with Boundary-Value Corrections
• Finite Element Methods with B-Splines
• A fixed‐grid b‐spline finite element technique for fluid–structure interaction
• Analysis of the shifted boundary method for the Poisson problem in domains with corners