The estimation of truncation error by \(\tau\)-estimation for Chebyshev spectral collocation method

DOI10.1007/s10915-013-9698-8zbMath1282.65125OpenAlexW2005500071MaRDI QIDQ395339

Mohammad Hasan, H. S. Yoon

Publication date: 29 January 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-013-9698-8

zbMATH Keywords

truncation errorspectral methodsuncertainty estimator\(\tau\)-estimation

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (9)

A functional oriented truncation error adaptation method ⋮ Comparisons of \(p\)-adaptation strategies based on truncation- and discretisation-errors for high order discontinuous Galerkin methods ⋮ \texttt{HORSES3D}: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications ⋮ Truncation error estimation in the p-anisotropic discontinuous Galerkin spectral element method ⋮ Quasi-a priori truncation error estimation in the DGSEM ⋮ A discontinuous Galerkin approximation for a wall-bounded consistent three-component Cahn-Hilliard flow model ⋮ Adaptation strategies for high order discontinuous Galerkin methods based on tau-estimation ⋮ The series expansion and Chebyshev collocation method for nonlinear singular two-point boundary value problems ⋮ A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods

Uses Software

• DLR PADGE
• GASpAR

Cites Work

• The estimation of truncation error by \(\tau \)-estimation revisited
• Least-squares spectral element solution of incompressible Navier-Stokes equations with adaptive refinement
• Adjoint-based error estimation and adaptive mesh refinement for the RANS and \(k-\omega\) turbulence model equations
• Adjoint-based \(h\)-\(p\) adaptive discontinuous Galerkin methods for the 2D compressible Euler equations
• Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations
• Dynamics of regularized cavity flow at high Reynolds numbers
• On the accuracy of multigrid truncation error estimates
• A weak Legendre collocation spectral method for the solution of the incompressible Navier-Stokes equations in unstructured quadrilateral subdomains.
• Adjoint error estimation and grid adaptation for functional outputs: Application to quasi-one-dimensional flow
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Adaptive mesh strategies for the spectral element method
• Benchmark spectral results on the lid-driven cavity flow
• Geophysical-astrophysical spectral-element adaptive refinement (GASpAR): object-oriented \(h\)-adaptive fluid dynamics simulation
• A numerical method for solving incompressible viscous flow problems
• The background of error estimation and adaptivity in finite element computations
• Multigrid Techniques
• Finite volume adaptive solutions using SIMPLE as smoother
• Implementing Spectral Methods for Partial Differential Equations
• $\tau$-Extrapolation---Theoretical Foundation, Numerical Experiment, and Application to Navier--Stokes Equations
• Optimal Decomposition of the Domain in Spectral Methods for Wave-Like Phenomena
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