Error Estimates of a Continuous Galerkin Time Stepping Method for Subdiffusion Problem

Abstract A continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a piecewise linear function t the test space based on discontinuous constant functions. We prove that proposed has convergence order $$O(\tau ^{1+ \alpha }), \, \in (0, 1)$$ O ( τ 1 + α ) , ∈ 0 general sectorial elliptic operators nonsmooth data by using Laplace transform method, where $$\tau $$ step size. This higher than orders of popular convolution quadrature methods (e.g., Lubich’s methods) L-type L1 method), which have only )$$ data. Numerical examples are given to verify robustness discretization schemes with respect regularity.