Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems

DOI10.1007/978-3-319-01818-8_8zbMath1282.65110OpenAlexW63761929MaRDI QIDQ5396557

Emmanuil H. Georgoulis, Edward J. C. Hall, Charalambos G. Makridakis

Publication date: 31 January 2014

Published in: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-01818-8_8

zbMATH Keywords

numerical experimentsdiscontinous Galerkin methoda posteriori error boundsfirst-order linear hyperbolic problem

Mathematics Subject Classification ID

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) First-order hyperbolic equations (35L02)

Related Items

Adaptive least-squares finite element methods for linear transport equations based on an H(div) flux reformulation, A posteriori analysis for dynamic model adaptation in convection-dominated problems, Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data, Guaranteed and robust L²-norm a posteriori error estimates for 1D linear advection problems, A posteriori error analysis for implicit-explicit \textit{hp}-discontinuous Galerkin timestepping methods for semilinear parabolic problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A unifying theory of a posteriori error control for discontinuous Galerkin FEM
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws
• Energy norm a posteriori error estimation for discontinuous Galerkin methods.
• A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
• A posteriori error analysis for higher order dissipative methods for evolution problems
• hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
• Reconstruction-Based a Posteriori Error Estimators for the Transport Equation
• A Posteriori Error Estimation for Interior Penalty Finite Element Approximations of the Advection-Reaction Equation
• Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity
• Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes
• An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Local Error Estimates for a Finite Element Method for Hyperbolic and Convection-Diffusion Equations
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• Stabilizedhp-Finite Element Methods for First-Order Hyperbolic Problems
• Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
• An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Ana posteriorierror bound for discontinuous Galerkin approximations of convection–diffusion problems
• Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
• Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory