Two-scale composite finite element method for Dirichlet problems on complicated domains

DOI10.1007/s00211-005-0654-xzbMath1108.65118OpenAlexW2053202794MaRDI QIDQ818795

Stefan A. Sauter, Anton Smolianski, Mathias Rech

Publication date: 21 March 2006

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-005-0654-x

zbMATH Keywords

convergenceerror estimatesnumerical experimentsPoisson equationdomains with complicated micro-structure

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)

Related Items (14)

A Multiscale Finite Element Method for Oscillating Neumann Problem on Rough Domain ⋮ Composite finite elements for elliptic interface problems ⋮ Error Estimates for Two-Scale Composite Finite Element Approximations of Nonlinear Parabolic Equations ⋮ A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub‐modeling ⋮ A combined finite element method for elliptic problems posted in domains with rough boundaries ⋮ Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains ⋮ Finite element methods for the Stokes problem on complicated domains ⋮ Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods ⋮ Composite finite element approximation for parabolic problems in nonconvex polygonal domains ⋮ Coarsening of boundary-element spaces ⋮ A multiscale finite element method for partial differential equations posed in domains with rough boundaries ⋮ Two-scale composite finite element method for parabolic problems with smooth and nonsmooth initial data ⋮ Error estimates for two-scale composite finite element approximations of parabolic equations with measure data in time for convex and nonconvex polygonal domains ⋮ hp –Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains

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• Coarse grid spaces for domains with a complicated boundary
• The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
• An algorithm for coarsening unstructured meshes
• Composite finite elements for problems containing small geometric details. II: Implementation and numerical results

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