Polynomial extensions of compatible polynomial traces in three dimensions

DOI10.1016/S0045-7825(94)80028-6zbMath0826.65097MaRDI QIDQ1892466

Faker Ben Belgacem

Publication date: 26 November 1995

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

condition numberspectral methods\(p\) finite element methodsstability estimatesdomain decomposition preconditionerscompatible polynomial tracesSobolev space scalesspectral finite element methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) 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) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items

Fast domain decomposition algorithm discretizations of 3-d elliptic equations by spectral elements, Stable Lifting of Polynomial Traces on Triangles, Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D, $H^2$-Stable Polynomial Liftings on Triangles, Local high-order regularization and applications to \(hp\)-methods, The lifting of polynomial traces revisited, Polynomial extension operators for $H^1$, $\boldsymbol {\mathit {H}}(\mathbf {curl})$ and $\boldsymbol {\mathit {H}}(\mathbf {div})$-spaces on a cube, Explicit polynomial preserving trace liftings on a triangle, Additive schwarz methods for indefinite hypersingular integral equations in R³- the p-version

Cites Work

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• Parallel algorithms for the capacitance matrix method in domain decompositions
• On a class of interpolation spaces
• Relèvement polynômial de traces et applications
• The $h-p$ version of the finite element method with quasiuniform meshes
• The Schwarz Algorithm for Spectral Methods