Analysis of Finite Element Domain Embedding Methods for Curved Domains using Uniform Grids

DOI10.1137/060671681zbMath1180.65157OpenAlexW2070756681MaRDI QIDQ3654392

Sheng Zhang

Publication date: 6 January 2010

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/7c8ea6f8b3a30d346d5b9e1cd798cbc6bd235b09

zbMATH Keywords

convergenceDirichlet problemfinite elementerror boundsPoisson equationNeumann problemfictitious domainnumerical resultfast Poisson solveruniform meshcurved boundarydomain embeddingRobin problems

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) Fictitious domain methods for boundary value problems involving PDEs (65N85) Method of contraction of the boundary for boundary value problems involving PDEs (65N45)

Related Items (10)

Penalty method for the stationary Navier-Stokes problems under the slip boundary condition ⋮ Penalty method with P1/P1 finite element approximation for the Stokes equations under the slip boundary condition ⋮ The fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition ⋮ The fictitious domain method with \(H^1\)-penalty for the Stokes problem with Dirichlet boundary condition ⋮ The Crouzeix-Raviart element for the Stokes equations with the slip boundary condition on a curved boundary ⋮ Analysis of the fictitious domain method with penalty for elliptic problems ⋮ The fictitious domain method with penalty for the parabolic problem in moving-boundary domain: the error estimate of penalty and the finite element approximation ⋮ Error estimates of fictitious domain method with an \(H^1\) penalty approach for elliptic problems ⋮ An augmented interface approach in fictitious domain methods ⋮ Analysis of the Fictitious Domain Method with anL²-Penalty for Elliptic Problems

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