Difference quotient estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear convection-diffusion equations

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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)

Cites Work

Smoothness-increasing accuracy-conserving (SIAC) filters for discontinuous Galerkin solutions: application to structured tetrahedral meshes
Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement
Analysis of space-time discontinuous Galerkin method for nonlinear convection-diffusion problems
Smoothness-increasing accuracy-conserving (SIAC) filters for derivative approximations of discontinuous Galerkin (DG) solutions over nonuniform meshes and near boundaries
Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
Asymptotically exact posteriori error estimates for the local discontinuous Galerkin method applied to nonlinear convection-diffusion problems
On a one-sided post-processing technique for the discontinuous Galerkin methods
Smoothness-increasing accuracy-conserving (SIAC) filtering for discontinuous Galerkin solutions: improved errors versus higher-order accuracy
Negative-order norm estimates for nonlinear hyperbolic conservation laws
Smoothness-increasing accuracy-conserving (SIAC) filtering for discontinuous Galerkin solutions over nonuniform meshes: superconvergence and optimal accuracy
Discontinuous Galerkin method for hyperbolic equations involving \(\delta \)-singularities: negative-order norm error estimates and applications
Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems
Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data
Exploiting Superconvergence Through Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering
Accuracy-enhancement of discontinuous Galerkin solutions for convection-diffusion equations in multiple-dimensions
Smoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions over Structured Triangular Meshes
Postprocessing for the Discontinuous Galerkin Method over Nonuniform Meshes
Higher Order Local Accuracy by Averaging in the Finite Element Method
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
A Superconvergent Local Discontinuous Galerkin Method for Nonlinear Fourth-Order Boundary-Value Problems
Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments

This page was built for publication: Difference quotient estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear convection-diffusion equations