TY - JOUR
T1 - Error Estimates for Approximations of Time-Fractional Biharmonic Equation with Nonsmooth Data
AU - Al-Maskari, Mariam
AU - Karaa, Samir
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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PY - 2022/8/22
Y1 - 2022/8/22
N2 - We consider a time-fractional biharmonic equation involving a Caputo derivative in time of fractional order α∈ (0 , 1 ) and a locally Lipschitz continuous nonlinearity. Local and global existence of solutions is discussed and detailed regularity results are provided. A finite element method in space combined with a backward Euler convolution quadrature in time is analyzed. Our objective is to allow initial data of low regularity compared to the number of derivatives occurring in the governing equation. Using a semigroup type approach, error estimates of optimal order are derived for solutions with smooth and nonsmooth initial data. Numerical tests are presented to validate the theoretical results.
AB - We consider a time-fractional biharmonic equation involving a Caputo derivative in time of fractional order α∈ (0 , 1 ) and a locally Lipschitz continuous nonlinearity. Local and global existence of solutions is discussed and detailed regularity results are provided. A finite element method in space combined with a backward Euler convolution quadrature in time is analyzed. Our objective is to allow initial data of low regularity compared to the number of derivatives occurring in the governing equation. Using a semigroup type approach, error estimates of optimal order are derived for solutions with smooth and nonsmooth initial data. Numerical tests are presented to validate the theoretical results.
KW - Biharmonic equation
KW - Convolution quadrature
KW - Finite element method
KW - Nonsmooth initial data
KW - Optimal error estimate
KW - Semilinear time-fractional equation
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U2 - 10.1007/s10915-022-01971-z
DO - 10.1007/s10915-022-01971-z
M3 - Article
AN - SCOPUS:85136537449
SN - 0885-7474
VL - 93
SP - 8
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
M1 - 1
ER -