Idempotent filtering in spectral and spectral element methods

DOI10.1016/j.jcp.2006.05.014zbMath1106.65089OpenAlexW2086195196MaRDI QIDQ860281

Jan S. Hesthaven, Mark H. Carpenter, Alex Kanevsky

Publication date: 9 January 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2006.05.014

zbMATH Keywords

numerical resultsinverse problemconservation lawsnumerical examplesHelmholtz equationnonlinear ill-posed problemoptimization method

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Cites Work

• Unnamed Item
• Unnamed Item
• Family of spectral filters for discontinuous problems
• On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
• Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information
• Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
• Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
• Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow
• Filter-based stabilization of spectral element methods
• Filtering in Legendre spectral methods
• Stability of the Fourier Method
• The Fourier Method for Nonsmooth Initial Data
• On the Gibbs Phenomenon and Its Resolution
• From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
• High–order nodal discontinuous Galerkin methods for the Maxwell eigenvalue problem
• Spectral methods for hyperbolic problems
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions