Superconvergence of the discontinuous Galerkin method for nonlinear second-order initial-value problems for ordinary differential equations
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Publication:512299
DOI10.1016/j.apnum.2017.01.007zbMath1358.65045OpenAlexW2573944670MaRDI QIDQ512299
Publication date: 24 February 2017
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2017.01.007
numerical exampleinitial value problemdiscontinuous Galerkin methodsuperconvergencea priori error estimatesnonlinear second-order ordinary differential equations equation
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)
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Cites Work
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- Analysis of a posteriori error estimates of the discontinuous Galerkin method for nonlinear ordinary differential equations
- A local discontinuous Galerkin method for the second-order wave equation
- Asymptotically exact a posteriori LDG error estimates for one-dimensional 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 discontinuous Galerkin method for higher-order ordinary differential equations
- Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
- Parallel, adaptive finite element methods for conservation laws
- A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
- A superconvergence result for discontinuous Galerkin methods applied to elliptic problems.
- Parallel adaptive \(hp\)-refinement techniques for conservation laws
- \textit{A posteriori} error estimates for a discontinuous Galerkin method applied to one-dimensional nonlinear scalar conservation laws
- The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis
- 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
- Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- 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
- 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
- An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems
- An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
- 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
- Adaptivity and Error Estimation for Discontinuous Galerkin Methods
- A special stability problem for linear multistep methods
