Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation

Abstract

Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.

Keywords

• Subdiffusion equation
• Weighted and shifted Grünwald formula
• Finite element method
• Superconvergence estimate