Variable-time-step BDF2 nonconforming VEM for coupled Ginzburg-Landau equations

Abstract

In this paper, we solve the coupled Ginzburg-Landau equations by using a linearized variable-time-step second order backward differentiation formula in time combining with a nonconforming virtual element method in space. Based on the techniques of the discrete orthogonal convolution kernels and the discrete complementary convolution kernels, the unconditional optimal L2-norm error estimate of the fully discrete scheme was presented by using the error splitting technique under the mild restriction on the ratio of adjacent time-steps ratios. Finally, numerical experiments illustrate the correctness of our theoretical analysis.