Preconditioning of the \(p\)-version of the finite element method

DOI10.1016/S0045-7825(97)00090-XzbMath0907.65121OpenAlexW2070689862MaRDI QIDQ1267874

K. Appert

Publication date: 13 October 1998

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

Full work available at URL: https://doi.org/10.1016/s0045-7825(97)00090-x

zbMATH Keywords

Schur complementpreconditioningdomain decomposition methodcondition numberssecond-order elliptic equations\(p\)-version finite element 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)

Related Items

Multiresolution weighted norm equivalencies and applications ⋮ Fast domain decomposition algorithm discretizations of 3-d elliptic equations by spectral elements ⋮ Spectral discretizations of 3-D elliptic problems and fast domain decomposition methods ⋮ Sparse shape functions for tetrahedral \(p\)-FEM using integrated Jacobi polynomials ⋮ Optimal extensions on tensor-product meshes ⋮ A domain decomposition preconditioner for \(p\)-FEM discretizations of two-dimensional elliptic problems ⋮ New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials ⋮ Wavelet solvers for \(hp\)-FEM discretizations in 3D using hexahedral elements ⋮ Equilibrated residual error estimates are \(p\)-robust ⋮ Domain decomposition preconditioning in the hierarchical \(p\)-version of the finite element method ⋮ Additive Schwarz algorithms for solving \(hp\)-version finite element systems on triangular meshes

Uses Software

• symrcm

Cites Work

• \(p\)-version of mixed finite element methods for Stokes-like problems
• Basis function selection and preconditioning high degree finite element and spectral methods
• A finite element - capacitance method for elliptic problems on regions partitioned into subregions
• Iterative solvers by substructuring for the \(p\)-version finite element method
• Polynomial interpolation results in Sobolev spaces
• Additive Schwarz methods for the \(p\)-version finite element method
• Schwarz methods with local refinement for the \(p\)-version finite element method
• Stabilization of spectral methods by finite element bubble functions
• Preconditioned Chebyshev collocation methods and triangular finite elements
• The choice of high order coordinate functions and preconditioning in frames of the method of domain decomposition
• Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems
• The problem of selecting the shape functions for ap-type finite element
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• On the Sharpness of L 2 -Error Estimates of H 1 0 -Projections Onto Subspaces of Piecewise High-Order Polynomials
• Parallel Domain Decomposition Solver for Adaptive hp Finite Element Methods
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• Preconditioning Legendre Spectral Collocation Approximations to Elliptic Problems
• A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes
• Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations
• Equivalent Norms for Sobolev Spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item