Finite element method for fractional order parabolic obstacle problem with nonlinear source term

Abstract

This paper considers the finite element method for a fractional order parabolic obstacle problem in time with a nonlinear source term. An error estimation of the spatially semi-discrete problem is discussed. A fully discrete problem is proposed by introducing the finite difference approximation for the time variable. The L2-unconditional stability and convergence of the approximate solution have been proven.

Keywords

• Fractional obstacle problem
• Grunwald–Letnikov derivative
• Stability
• Error estimation