Biquadratic finite volume element methods based on optimal stress points for parabolic problems

摘要

In this paper, the semi-discrete and full discrete biquadratic finite volume element schemes based on optimal stress points for a class of parabolic problems are presented. Optimal order error estimates in H1 and L2 norms are derived. In addition, the superconvergences of numerical gradients at optimal stress points are also discussed. A numerical experiment confirms some results of theoretical analysis.