research-article

Convergence Analysis of a Petrov–Galerkin Method for Fractional Wave Problems with Nonsmooth Data

Authors:

Xiaoping XieAuthors Info & Claims

Volume 80, Issue 2

Pages 957 - 992

https://doi.org/10.1007/s10915-019-00962-x

Published: 01 August 2019 Publication History

Abstract

This paper analyzes the convergence of a Petrov–Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the time fractional wave problem are firstly established. Then an optimal convergence analysis with nonsmooth data is derived. Moreover, several numerical experiments are presented to validate the theoretical results.

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Cited By

Ramezani MMokhtari RYan Y(2024)Correction of a High-Order Numerical Method for Approximating Time-Fractional Wave EquationJournal of Scientific Computing10.1007/s10915-024-02625-y100:3Online publication date: 22-Jul-2024
https://dl.acm.org/doi/10.1007/s10915-024-02625-y
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
Zhou QFeng M(2022)Analysis of a Full Discretization for a Fractional/Normal Diffusion Equation with Rough Dirichlet Boundary DataJournal of Scientific Computing10.1007/s10915-022-01875-y92:1Online publication date: 11-Jun-2022
https://dl.acm.org/doi/10.1007/s10915-022-01875-y
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Convergence Analysis of a Petrov–Galerkin Method for Fractional Wave Problems with Nonsmooth Data

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Published In

cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 80, Issue 2

Aug 2019

652 pages

ISSN:0885-7474

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Copyright © 2019 Springer Science+Business Media, LLC, part of Springer Nature.

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Plenum Press

United States

Publication History

Published: 01 August 2019

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Cited By

Ramezani MMokhtari RYan Y(2024)Correction of a High-Order Numerical Method for Approximating Time-Fractional Wave EquationJournal of Scientific Computing10.1007/s10915-024-02625-y100:3Online publication date: 22-Jul-2024
https://dl.acm.org/doi/10.1007/s10915-024-02625-y
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
Zhou QFeng M(2022)Analysis of a Full Discretization for a Fractional/Normal Diffusion Equation with Rough Dirichlet Boundary DataJournal of Scientific Computing10.1007/s10915-022-01875-y92:1Online publication date: 11-Jun-2022
https://dl.acm.org/doi/10.1007/s10915-022-01875-y
Luo HXie X(2022)Optimal Error Estimates of a Time-Spectral Method for Fractional Diffusion Problems with Low Regularity DataJournal of Scientific Computing10.1007/s10915-022-01791-191:1Online publication date: 24-Feb-2022
https://dl.acm.org/doi/10.1007/s10915-022-01791-1
Zhou QLi B(2021)Temporally Semidiscrete Approximation of a Dirichlet Boundary Control for a Fractional/Normal Evolution Equation with a Final ObservationJournal of Scientific Computing10.1007/s10915-021-01522-y88:1Online publication date: 21-May-2021
https://dl.acm.org/doi/10.1007/s10915-021-01522-y
Li BLuo HXie X(2020)A space-time finite element method for fractional wave problemsNumerical Algorithms10.1007/s11075-019-00857-w85:3(1095-1121)Online publication date: 4-Jan-2020
https://dl.acm.org/doi/10.1007/s11075-019-00857-w
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
Zhou BChen XLi D(2020)Nonuniform Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Parabolic EquationsJournal of Scientific Computing10.1007/s10915-020-01350-685:2Online publication date: 27-Oct-2020
https://dl.acm.org/doi/10.1007/s10915-020-01350-6
Li BWang TXie X(2020)Analysis of a Time-Stepping Discontinuous Galerkin Method for Fractional Diffusion-Wave Equations with Nonsmooth DataJournal of Scientific Computing10.1007/s10915-019-01118-782:1Online publication date: 7-Jan-2020
https://dl.acm.org/doi/10.1007/s10915-019-01118-7

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