Negative-order norm estimates for nonlinear hyperbolic conservation laws

DOI10.1007/s10915-012-9668-6zbMath1266.65155OpenAlexW2112082878MaRDI QIDQ1945378

Yan Xu, Liangyue Ji, Jennifer K. Ryan

Publication date: 8 April 2013

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

Full work available at URL: https://doi.org/10.1007/s10915-012-9668-6

zbMATH Keywords

error estimatesdiscontinuous Galerkin methodsuperconvergencenonlinear hyperbolic conservation lawsB-splinespost-processingnegative-order normSIAC filteringsmoothness-increasing accuracy-conserving filter

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Unnamed Item
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. II: A posteriori error estimation
• Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
• Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
• Lectures on the finite element method. Notes by S. Kesavan, Akhil Ranjan, M. Vanninathan
• Lectures on nonlinear hyperbolic differential equations
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis
• Accuracy-enhancement of discontinuous Galerkin solutions for convection-diffusion equations in multiple-dimensions
• Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Improving Discontinuous Galerkin Solutions
• Smoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions over Structured Triangular Meshes
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Higher Order Local Accuracy by Averaging in the Finite Element Method
• Propagation of error into regions of smoothness for accurate difference approximations to hyperbolic equations
• Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations
• High Order Local Approximations to Derivatives in the Finite Element Method
• Construction of adjoint operators in non-linear problems of mathematical physics
• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• A Local Discontinuous Galerkin Method for KdV Type Equations
• Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws
• Error Estimates to Smooth Solutions of Runge–Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws

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