A mixed virtual element method for the time-fractional fourth-order subdiffusion equation

We propose and analyze a mixed virtual element method for time-fractional fourth-order subdiffusion equation involving the Caputo fractional derivative on polygonal meshes, whose solutions display a typical weak singularity at the initial time. By introducing an auxiliary variable sigma = Delta u, then the fourth-order equation can be split into the coupled system of two second-order equations. Based on the L1 scheme on a graded temporal mesh, the unconditional stability of the fully discrete is proved for two variables; and the priori error estimates are derived in L-2 norm for the scalar unknown u and the variable sigma, respectively. Moreover, the priori error result in H-1 semi-norm for the scalar unknown u also is obtained. Finally, a numerical calculation is implemented to verify the theoretical results.