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Article: Homogenization of time-fractional diffusion equations with periodic coefficients
Title | Homogenization of time-fractional diffusion equations with periodic coefficients |
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Authors | |
Keywords | First order approximation Error estimate 2-scale asymptotic expansion Time-fractional diffusion Homogenization |
Issue Date | 2020 |
Citation | Journal of Computational Physics, 2020, v. 408, article no. 109231 How to Cite? |
Abstract | © 2020 Elsevier Inc. We consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data a(x)∈L2(D) in a bounded domain D⊂Rd with a sufficiently smooth boundary. We analyze the homogenized solution under the assumption that the diffusion coefficient κϵ(x) is smooth and periodic with the period ϵ>0 being sufficiently small. We derive that its first order approximation measured by both pointwise-in-time in L2(D) and Lp((θ,T);H1(D)) for p∈[1,∞) and θ∈(0,T) has a convergence rate of O(ϵ1/2) when the dimension d≤2 and O(ϵ1/6) when d=3. Several numerical tests are presented to demonstrate the performance of the first order approximation. |
Persistent Identifier | http://hdl.handle.net/10722/287015 |
ISSN | 2023 Impact Factor: 3.8 2023 SCImago Journal Rankings: 1.679 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Hu, Jiuhua | - |
dc.contributor.author | Li, Guanglian | - |
dc.date.accessioned | 2020-09-07T11:46:16Z | - |
dc.date.available | 2020-09-07T11:46:16Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Journal of Computational Physics, 2020, v. 408, article no. 109231 | - |
dc.identifier.issn | 0021-9991 | - |
dc.identifier.uri | http://hdl.handle.net/10722/287015 | - |
dc.description.abstract | © 2020 Elsevier Inc. We consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data a(x)∈L2(D) in a bounded domain D⊂Rd with a sufficiently smooth boundary. We analyze the homogenized solution under the assumption that the diffusion coefficient κϵ(x) is smooth and periodic with the period ϵ>0 being sufficiently small. We derive that its first order approximation measured by both pointwise-in-time in L2(D) and Lp((θ,T);H1(D)) for p∈[1,∞) and θ∈(0,T) has a convergence rate of O(ϵ1/2) when the dimension d≤2 and O(ϵ1/6) when d=3. Several numerical tests are presented to demonstrate the performance of the first order approximation. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Computational Physics | - |
dc.subject | First order approximation | - |
dc.subject | Error estimate | - |
dc.subject | 2-scale asymptotic expansion | - |
dc.subject | Time-fractional diffusion | - |
dc.subject | Homogenization | - |
dc.title | Homogenization of time-fractional diffusion equations with periodic coefficients | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.jcp.2020.109231 | - |
dc.identifier.scopus | eid_2-s2.0-85078050022 | - |
dc.identifier.volume | 408 | - |
dc.identifier.spage | article no. 109231 | - |
dc.identifier.epage | article no. 109231 | - |
dc.identifier.eissn | 1090-2716 | - |
dc.identifier.isi | WOS:000521731200022 | - |
dc.identifier.issnl | 0021-9991 | - |