Finite-difference preconditioners for superconsistent pseudospectral approximations

DOI10.1051/m2an:2007052zbMath1133.65103OpenAlexW2155769359MaRDI QIDQ5437452

Daniele Funaro, Lorella Fatone, Valentina Scannavini

Publication date: 21 January 2008

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2007__41_6_1021_0

zbMATH Keywords

numerical resultspreconditioningfinite differencesLebesgue constantspectral collocationsuperconsistencyadvection-diffusion boundary value problems

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items

Superconsistent collocation methods with applications to convection-dominated convection-diffusion equations, A superconsistent collocation method for high Reynolds number flows, A convergence analysis for the superconsistent Chebyshev method, Optimal Collocation Nodes for Fractional Derivative Operators

Uses Software

• Eigtool

Cites Work

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• Some remarks about the collocation method on a modified Legendre grid
• Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation
• A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm
• Spectral methods for problems in complex geometries
• Spectral and pseudo-spectral methods for parabolic problems with non periodic boundary conditions
• Spectral elements for transport-dominated equations
• Superconsistent discretizations
• On Fourier series of a discrete Jacobi--Sobolev inner product
• A short survey on preconditioning techniques in spectral calculations
• A convergence analysis for the superconsistent Chebyshev method
• Boundary and interface conditions within a finite element preconditioner for spectral methods
• Preconditioning Chebyshev Spectral Collocation by Finite-Difference Operators
• Preconditioning Chebyshev Spectral Collocation Method for Elliptic Partial Differential Equations
• A superconsistent Chebyshev collocation method for second-order differential operators