A posteriori error estimates and adaptivity for the discontinuous Galerkin solutions of nonlinear second-order initial-value problems

DOI10.1016/j.apnum.2017.06.001zbMath1372.65223OpenAlexW2626192092MaRDI QIDQ2402557

Mahboub Baccouch

Publication date: 8 September 2017

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2017.06.001

zbMATH Keywords

adaptive mesh refinementdiscontinuous Galerkin methodsuperconvergencea posteriori error estimatesnumerical resultnonlinear second-order initial value problems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (4)

Superconvergent postprocessing of the \(C^1\)-conforming finite element method for fourth-order boundary value problems ⋮ Superconvergent postprocessing of the continuous Galerkin time stepping method for nonlinear initial value problems with application to parabolic problems ⋮ Optimal error estimates and superconvergence of an ultra weak discontinuous Galerkin method for fourth-order boundary-value problems ⋮ The discontinuous Galerkin method for general nonlinear third-order ordinary differential equations

Uses Software

• Mulprec

Cites Work

• Analysis of a posteriori error estimates of the discontinuous Galerkin method for nonlinear ordinary differential equations
• Superconvergence and a posteriori error estimates for the LDG method for convection-diffusion problems in one space dimension
• A local discontinuous Galerkin method for the second-order wave equation
• The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis
• The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. II: A posteriori error estimation
• Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems
• Superconvergence of the discontinuous Galerkin method for nonlinear second-order initial-value problems for ordinary differential equations
• Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. II: A posteriori error estimation
• Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• A discontinuous Galerkin method for higher-order ordinary differential equations
• Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• A discontinuous \(hp\) finite element method for convection-diffusion problems
• Parallel, adaptive finite element methods for conservation laws
• A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
• \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws
• A superconvergence result for discontinuous Galerkin methods applied to elliptic problems.
• A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems
• A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
• Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems
• A parallel \(hp\)-adaptive discontinuous Galerkin method for hyperbolic conservation laws
• Parallel adaptive \(hp\)-refinement techniques for conservation laws
• A superconvergent local discontinuous Galerkin method for elliptic problems
• \textit{A posteriori} error estimates for a discontinuous Galerkin method applied to one-dimensional nonlinear scalar conservation laws
• A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids
• Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis
• A posteriori local discontinuous Galerkin error estimation for two-dimensional convection-diffusion problems
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations
• Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation
• Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations
• Numerical Methods in Scientific Computing, Volume I
• Discontinuous Polynomial Approximations in the Theory of One-Step, Hybrid and Multistep Methods for Nonlinear Ordinary Differential Equations
• An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
• Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Discontinuous Galerkin Methods for Ordinary Differential Equations
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
• Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
• An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• hp‐version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy
• Error Estimates for Finite Element Methods for Scalar Conservation Laws
• Superconvergence of Discontinuous Galerkin Methods for Scalar Nonlinear Conservation Laws in One Space Dimension
• Analysis of Optimal Superconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations
• Optimal a Posteriori Error Estimates of the Local Discontinuous Galerkin Method for Convection-Diffusion Problems in One Space Dimension
• Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments
• Adaptivity and Error Estimation for Discontinuous Galerkin Methods
• Superconvergence of the local discontinuous galerkin method applied to the one‐dimensional second‐order wave equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A posteriori error estimates and adaptivity for the discontinuous Galerkin solutions of nonlinear second-order initial-value problems