A remark on least-squares mixed element methods for reaction–diffusion problems

In this paper, we propose a least-squares mixed element procedure for a reaction–diffusion problem based on the first-order system. By selecting the least-squares functional properly, the resulting procedure can be split into two independent symmetric positive definite schemes, one of which is for the unknown variable and the other of which is for the unknown flux variable, which lead to the optimal order H1(Ω)H1(Ω) and L2(Ω)L2(Ω) norm error estimates for the primal unknown and optimal H(div;Ω)H(div;Ω) norm error estimate for the unknown flux. Finally, we give some numerical examples.