A Hierarchical Domain Decomposition Preconditioner forh-PFinite Element Approximation on Locally Refined Meshes

DOI10.1137/S1064827594272578zbMath0860.65111OpenAlexW1984104476MaRDI QIDQ4717314

Mark Ainsworth

Publication date: 21 April 1997

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s1064827594272578

zbMATH Keywords

numerical examplesdomain decompositionfinite elementcondition numberpreconditioner\(h\)-\(p\) refinementhierarchical basis method

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations ⋮ Fully automatic \(hp\)-adaptivity in three dimensions ⋮ Rapid error reduction for block Gauss-Seidel based onp-hierarchical basis ⋮ Multilevel preconditioned QMR methods for unstructured mesh computation ⋮ Error estimates and adaptive finite element methods ⋮ Integration of \(hp\)-adaptivity and a two-grid solver for elliptic problems ⋮ On the accuracy ofp-version elements for the Reissner-Mindlin plate problem ⋮ Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers ⋮ An improved multigrid solver for the \(p\)-hierarchical basis finite element method using a space decomposition smoother ⋮ Domain decomposition preconditioners for \(p\) and \(hp\) finite element approximation of Stokes equations ⋮ Dynamically adapted mesh refinement for combustion front tracking.

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