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 u 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.