Pointwise-in-time a posteriori error control for time-fractional parabolic equations

Natalia Kopteva

doi:10.1016/j.aml.2021.107515

Pointwise-in-time a posteriori error control for time-fractional parabolic equations

Natalia Kopteva

Research output: Contribution to journal › Article › peer-review

Abstract

For time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwise-in-time a posteriori error bounds in the spatial L₂ and L_∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2−α in the presence of solution singularities.

Original language	English
Article number	107515
Journal	Applied Mathematics Letters
Volume	123
DOIs	https://doi.org/10.1016/j.aml.2021.107515
Publication status	Published - Jan 2022

Keywords

Fractional-order parabolic equation
Graded meshes
L1 scheme
Optimal convergence rates
Pointwise-in-time a posteriori error bounds

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10.1016/j.aml.2021.107515

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title = "Pointwise-in-time a posteriori error control for time-fractional parabolic equations",

abstract = "For time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwise-in-time a posteriori error bounds in the spatial L2 and L∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2−α in the presence of solution singularities.",

keywords = "Fractional-order parabolic equation, Graded meshes, L1 scheme, Optimal convergence rates, Pointwise-in-time a posteriori error bounds",

author = "Natalia Kopteva",

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year = "2022",

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AB - For time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwise-in-time a posteriori error bounds in the spatial L2 and L∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2−α in the presence of solution singularities.

KW - Fractional-order parabolic equation

KW - Graded meshes

KW - L1 scheme

KW - Optimal convergence rates

KW - Pointwise-in-time a posteriori error bounds

UR - https://www.scopus.com/pages/publications/85112720383

U2 - 10.1016/j.aml.2021.107515

DO - 10.1016/j.aml.2021.107515

M3 - Article

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SN - 0893-9659

VL - 123

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 107515

ER -

Pointwise-in-time a posteriori error control for time-fractional parabolic equations

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