research-article

Analysis of a Time-Stepping Discontinuous Galerkin Method for Fractional Diffusion-Wave Equations with Nonsmooth Data

Authors:

Xiaoping XieAuthors Info & Claims

Journal of Scientific Computing, Volume 82, Issue 1

https://doi.org/10.1007/s10915-019-01118-7

Published: 07 January 2020 Publication History

Abstract

This paper analyzes a time-stepping discontinuous Galerkin method for fractional diffusion-wave problems. This method uses piecewise constant functions in the temporal discretization and continuous piecewise linear functions in the spatial discretization. Nearly optimal convergence with respect to the regularity of the solution is established when the source term is nonsmooth, and nearly optimal convergence rate

ln (1 / τ) (\sqrt{ln (1 / h)} h^{2} + τ)

is derived under appropriate regularity assumption on the source term. Convergence is also established without smoothness assumption on the initial value. Finally, numerical experiments are performed to verify the theoretical results.

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Cited By

Lyu PVong S(2022)A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave EquationsJournal of Scientific Computing10.1007/s10915-022-02000-993:1Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10915-022-02000-9
Li BWang TXie X(2020)Numerical Analysis of Two Galerkin Discretizations with Graded Temporal Grids for Fractional Evolution EquationsJournal of Scientific Computing10.1007/s10915-020-01365-z85:3Online publication date: 22-Nov-2020
https://dl.acm.org/doi/10.1007/s10915-020-01365-z

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Published In

cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 82, Issue 1

Jan 2020

605 pages

ISSN:0885-7474

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© Springer Science+Business Media, LLC, part of Springer Nature 2020.

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Plenum Press

United States

Publication History

Published: 07 January 2020

Accepted: 31 December 2019

Revision received: 26 November 2019

Received: 29 April 2019

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National Natural Science Foundation of China

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Cited By

Lyu PVong S(2022)A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave EquationsJournal of Scientific Computing10.1007/s10915-022-02000-993:1Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10915-022-02000-9
Li BWang TXie X(2020)Numerical Analysis of Two Galerkin Discretizations with Graded Temporal Grids for Fractional Evolution EquationsJournal of Scientific Computing10.1007/s10915-020-01365-z85:3Online publication date: 22-Nov-2020
https://dl.acm.org/doi/10.1007/s10915-020-01365-z

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