LSIAC-MRA for nonuniform meshes and applications to mesh adaptivity

Numerical smoothing, curve fitting (65D10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Cites Work

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Smoothness-increasing accuracy-conserving (SIAC) filtering and quasi-interpolation: a unified view
Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemes
Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations
One-sided position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering over uniform and non-uniform meshes
A practical guide to splines
Adaptive multiresolution schemes for shock computations
Hexagonal smoothness-increasing accuracy-conserving filtering
Wavelets and adaptive grids for the discontinuous Galerkin method
Adaptive multiscale schemes for conservation laws
Adaptive solution of partial differential equations in multiwavelet bases
On a one-sided post-processing technique for the discontinuous Galerkin methods
Adaptive characteristic length for L-SIAC filtering of FEM data
General spline filters for discontinuous Galerkin solutions
Adaptive multiresolution discontinuous Galerkin schemes for conservation laws: multi-dimensional case
A wavelet-free approach for multiresolution-based grid adaptation for conservation laws
Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations
Nonuniform Discontinuous Galerkin Filters via Shift and Scale
Adaptive multiresolution discontinuous Galerkin schemes for conservation laws
Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Improving Discontinuous Galerkin Solutions
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
Higher Order Local Accuracy by Averaging in the Finite Element Method
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
On the exponentially slow motion of a viscous shock
Multiresolution algorithms for the numerical solution of hyperbolic conservation laws
Enhanced MultiResolution Analysis for MultiDimensional Data Utilizing Line Filtering Techniques
A Combined-Mode Fourier Analysis of DG Methods for Linear Parabolic Problems
Multi-Dimensional Filtering: Reducing the Dimension Through Rotation
$h$-adaptation for high-order discontinuous Galerkin schemes built on local multiwavelet analysis

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