Superconvergence and \textit{a posteriori} error estimates of the DG method for scalar hyperbolic problems on Cartesian grids
From MaRDI portal
Publication:1664193
DOI10.1016/j.amc.2015.04.126zbMath1410.65443OpenAlexW397289539MaRDI QIDQ1664193
Publication date: 24 August 2018
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2015.04.126
discontinuous Galerkin methodsuperconvergencehyperbolic problemsderivative recovery techniqueCartesian grids\textit{a posteriori} error estimates
Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
A Recovery-Based Error Estimator for the Discontinuous Galerkin Method for Transient Linear Hyperbolic Conservation Laws on Cartesian Grids ⋮ A Posteriori Error Estimates for a Local Discontinuous Galerkin Approximation of Semilinear Second-Order Elliptic Problems on Cartesian Grids ⋮ A posteriori error estimates of a DG method for optimal control problems governed by the transport equation ⋮ Optimal error estimates and superconvergence of an ultra weak discontinuous Galerkin method for fourth-order boundary-value problems ⋮ Optimal superconvergence and asymptotically exact \textit{a posteriori} error estimator for the local discontinuous Galerkin method for linear elliptic problems on Cartesian grids ⋮ Two efficient and reliable a posteriori error estimates for the local discontinuous Galerkin method applied to linear elliptic problems on Cartesian grids
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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
- 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 posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems
- Optimal error estimate and superconvergence of the DG method for first-order hyperbolic problems
- Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
- A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
- Aspects of discontinuous Galerkin methods for hyperbolic conservation laws
- A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
- Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic 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 error estimates of recovery type for distributed convex optimal control problems
- A posteriori local discontinuous Galerkin error estimation for two-dimensional convection-diffusion problems
- General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
- Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
- Analysis of a Local Discontinuous Galerkin Method for Linear Time-Dependent Fourth-Order Problems
- Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity
- Symmetric positive linear differential equations
- A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
- Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes
- A simple error estimator and adaptive procedure for practical engineerng analysis
- An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
- A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
- An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
- L2 is a continuable initial condition for kreiss' mixed problems