Superconvergent error estimates for position-dependent smoothness-increasing accuracy-conserving (SIAC) post-processing of discontinuous Galerkin solutions

DOI10.1090/S0025-5718-2014-02835-4zbMath1300.65066MaRDI QIDQ3189421

P. van Slingerland, Liangyue Ji, Jennifer K. Ryan, Kees Vuik

Publication date: 10 September 2014

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

discontinuous Galerkin methoderror estimatehigh-order methodsnumerical resultsuper-convergencesmoothness-increasing accuracy-conserving filter

Mathematics Subject Classification ID

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) First-order hyperbolic equations (35L02)

Related Items (15)

Smoothness-increasing accuracy-conserving (SIAC) filtering and quasi-interpolation: a unified view ⋮ An adjoint-based super-convergent Galerkin approximation of eigenvalues ⋮ Shock regularization with smoothness-increasing accuracy-conserving Dirac-delta polynomial kernels ⋮ Capitalizing on superconvergence for more accurate multi-resolution discontinuous Galerkin methods ⋮ Superconvergence and the numerical flux: a study using the upwind-biased flux in discontinuous Galerkin methods ⋮ One-sided position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering over uniform and non-uniform meshes ⋮ Enhanced MultiResolution Analysis for MultiDimensional Data Utilizing Line Filtering Techniques ⋮ Explicit Least-Degree Boundary Filters for Discontinuous Galerkin ⋮ Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov-Maxwell equations ⋮ Hexagonal smoothness-increasing accuracy-conserving filtering ⋮ Magic SIAC Toolbox: A Codebase of Effective, Efficient, and Flexible Filters ⋮ Enhancing accuracy with a convolution filter: what works and why! ⋮ Smoothness-increasing accuracy-conserving (SIAC) filtering for discontinuous Galerkin solutions over nonuniform meshes: superconvergence and optimal accuracy ⋮ Exploiting Superconvergence Through Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering ⋮ Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space

Cites Work

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• A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• On a one-sided post-processing technique for the discontinuous Galerkin methods
• Efficient implementation of smoothness-increasing accuracy-conserving (SIAC) filters for discontinuous Galerkin solutions
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis
• Accuracy-enhancement of discontinuous Galerkin solutions for convection-diffusion equations in multiple-dimensions
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Improving Discontinuous Galerkin Solutions
• Smoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions over Structured Triangular Meshes
• Maximum-Norm Interior Estimates for Ritz-Galerkin Methods
• 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 discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels

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