IMPLEMENTATION OF HIGH-ORDER, DISCONTINUOUS GALERKIN TIME STEPPING FOR FRACTIONAL DIFFUSION PROBLEMS

DOI10.1017/S1446181120000152zbMath1457.65129arXiv2003.09805OpenAlexW3012754983MaRDI QIDQ5150284

William McLean

Publication date: 10 February 2021

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.09805

zbMATH Keywords

superconvergenceGauss quadraturereconstructionLegendre polynomialsfinite-element method

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) 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) Numerical integration (65D30) Fractional partial differential equations (35R11)

Related Items (4)

ON MULTIFRACTIONALITY OF SPHERICAL RANDOM FIELDS WITH COSMOLOGICAL APPLICATIONS ⋮ Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations ⋮ Error profile for discontinuous Galerkin time stepping of parabolic PDEs ⋮ FractionalTimeDG.jl

Uses Software

• GitHub

Cites Work

• Unnamed Item
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• The Variable-Order Discontinuous Galerkin Time Stepping Scheme for Parabolic Evolution Problems is Uniformly $L^\infty$-Stable
• Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations
• Galerkin Finite Element Methods for Parabolic Problems
• First Steps in Random Walks
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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