On the stability and performance of the \(p\)-version of the finite element method for first-order hyperbolic problems

DOI10.1016/0168-9274(94)00028-XzbMath0865.65069OpenAlexW2082559041MaRDI QIDQ1339346

V. Pereyra

Publication date: 1 December 1994

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(94)00028-x

zbMATH Keywords

stabilityconvergencefinite element methodnumerical experiments\(p\)-version\(h\)-versionfirst-order hyperbolic equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

The \(p\) and \(h-p\) versions of some finite element methods for Stokes' problem ⋮ \(p\)-version of mixed finite element methods for Stokes-like problems

Cites Work

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• Pointwise error estimates for a streamline diffusion finite element scheme
• Explicit finite element methods for scalar hyperbolic equations
• Shock capturing by the spectral viscosity method
• The p- and h-p versions of the finite element method. An overview
• Spectral Tau approximation of the two-dimensional Stokes problem
• A study of numerical methods for hyperbolic conservation laws with stiff source terms
• Finite Element Collocation Methods for First Order Systems
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Local Error Estimates for Discontinuous Solutions of Nonlinear Hyperbolic Equations
• The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
• Spectral Methods for Initial Boundary Value Problems—An Alternative Approach
• The $p$-version of the finite element method for elliptic equations of order $2l$
• Approximation Results for Orthogonal Polynomials in Sobolev Spaces
• The Approximation Theory for thep-Version of the Finite Element Method
• Analysis of a Continuous Finite Element Method for Hyperbolic Equations
• Stability Analysis of Spectral Methods for Hyperbolic Initial-Boundary Value Systems
• Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• Essentially Nonoscillatory Spectral Fourier Method for Shocks Wave Calculations
• A Stable Finite Element Method for Initial-Boundary Value Problems for First-Order Hyperbolic Systems
• The shock generation problem for a discrete gas with short-range repulsive forces
• A Finite Element Method for First Order Hyperbolic Equations
• An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation