Error Estimates for Approximations of Time-Fractional Biharmonic Equation with Nonsmooth Data

We consider a time-fractional biharmonic equation involving a Caputo derivative in time of fractional order alpha is an element of (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.

Automated summary

The paper discusses a time-fractional biharmonic equation involving a Caputo derivative in time and a locally Lipschitz continuous nonlinearity. The local and global existence of solutions as well as detailed regularity results are analyzed, along with a finite element method in space and a backward Euler convolution quadrature in time. The objective is to allow initial data of low regularity and optimal error estimates are derived for solutions with smooth and nonsmooth initial data using a semigroup approach. Numerical tests are presented to validate the theoretical results.