Split least-squares finite element methods for linear and nonlinear parabolic problems

In this paper, we propose some least-squares finite element procedures for linear and nonlinear parabolic equations based on first-order systems. By selecting the least-squares functional properly each proposed procedure can be split into two independent symmetric positive definite sub-procedures, one of which is for the primary unknown variable uu and the other is for the expanded flux unknown variable σ. Optimal order error estimates are developed. Finally we give some numerical examples which are in good agreement with the theoretical analysis.