Abstract
We consider a time-fractional biharmonic equation involving a Caputo derivative in time of fractional order \(\alpha \in (0,1)\) 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.
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Al-Maskari, M., Karaa, S. Error Estimates for Approximations of Time-Fractional Biharmonic Equation with Nonsmooth Data. J Sci Comput 93, 8 (2022). https://doi.org/10.1007/s10915-022-01971-z
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DOI: https://doi.org/10.1007/s10915-022-01971-z
Keywords
- Semilinear time-fractional equation
- Biharmonic equation
- Finite element method
- Convolution quadrature
- Optimal error estimate
- Nonsmooth initial data