Convergence and Superconvergence Analysis of a Nonconforming Finite Element Variable-Time-Step BDF2 Implicit Scheme for Linear Reaction-Diffusion Equations

In this paper, an effective fully-discrete implicit scheme for solving linear reaction-diffusion equations is constructed by using the variable-time-step two-step backward differentiation formula (VSBDF2) in time combining with the nonconforming finite element methods in space. By introducing a modified energy projection operator, a discrete Laplace operator, the discrete orthogonal convolution kernels, we obtain the optimal and sharp error estimates of order O(h^2+τ ^2) in L^2 -norm and O(h+τ ^2) in H^1 -norm under a mild restriction 0更多