An adaptive spectral least-squares scheme for the Burgers equation

DOI10.1007/s11075-007-9071-9zbMath1117.65139OpenAlexW2094766018MaRDI QIDQ885497

Wilhelm Heinrichs

Publication date: 14 June 2007

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-007-9071-9

zbMATH Keywords

numerical examplesfast Fourier transformsBurgers equationLeast-squaresexponential convergenceFilteringSpectral collocationAdaptive refinementleast-squares spectral collocation methodOver-collocation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (8)

Using generating functions to convert an implicit \((3,3)\) finite difference method to an explicit form on diffusion equation with different boundary conditions ⋮ An adaptive ALE method for underwater explosion simulations including cavitation ⋮ A novel numerical scheme for solving Burgers' equation ⋮ The pointwise estimates of a conservative difference scheme for Burgers' equation ⋮ On a weakly L‐stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic partial differential equations ⋮ An approximation method for solving Burgers' equation using Legendre wavelets ⋮ An hp‐adaptive pseudospectral method for solving optimal control problems ⋮ A numerical scheme for a class of generalized Burgers' equation based on Haar wavelet nonstandard finite difference method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Least-squares spectral collocation for the Navier-Stokes equations
• Least-squares finite element method for fluid dynamics
• An adaptive least-squares spectral collocation method with triangular elements for the incompressible Navier-Stokes equations
• Least-squares finite elements for the Stokes problem
• Spectral methods for problems in complex geometries
• Family of spectral filters for discontinuous problems
• Least-squares spectral collocation for discontinuous and singular perturbation problems
• A least-squares spectral element formulation for the Stokes problem
• Analysis of a discontinuous least squares spectral element method
• Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations
• The use of Chebyshev polynomials in the space-time least-squares spectral element method
• Least-squares spectral elements applied to the Stokes problem
• On the least-squares method
• Enhanced spectral viscosity approximations for conservation laws
• Higher-order Gauss-Lobatto integration for nonlinear hyperbolic equations
• A New Method of Stabilization for Singular Perturbation Problems with Spectral Methods
• A least-squares finite element method for incompressible Navier-Stokes problems
• Computational Gasdynamics
• On the Gibbs Phenomenon and Its Resolution

This page was built for publication: An adaptive spectral least-squares scheme for the Burgers equation