Analysis of the shifted boundary method for the Poisson problem in domains with corners

DOI10.1090/mcom/3641zbMath1472.65140arXiv2006.00872OpenAlexW3134671735MaRDI QIDQ4999468

Nabil M. Atallah, Claudio Canuto, Guglielmo Scovazzi

Publication date: 7 July 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.00872

zbMATH Keywords

convergence analysisfinite element methodsconsistency errorTaylor expansionsembedded methodsnon-smooth domainsimmersed boundary methodsweak boundary conditions

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (12)

The high-order shifted boundary method and its analysis ⋮ An unfitted finite element method using level set functions for extrapolation into deformable diffuse interfaces ⋮ Embedded domain reduced basis models for the shallow water hyperbolic equations with the shifted boundary method ⋮ The simple shifted fracture method ⋮ A blended shifted‐fracture/phase‐field framework for sharp/diffuse crack modeling ⋮ An enriched shifted boundary method to account for moving fronts ⋮ A divergence-free finite element method for the Stokes problem with boundary correction ⋮ 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 ⋮ A shifted boundary method based on extension operators ⋮ Analysis of the shifted boundary method for the Poisson problem in domains with corners

Uses Software

• CutFEM

Cites Work

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