Two new least-squares mixed finite element procedures for convection-dominated Sobolev equations

Two new least-squares mixed finite element procedures are formulated for solving convection-dominated Sobolev equations. Optimal H(div;Ω)×H1(Ω) norms error estimates are derived under the standard mixed finite spaces. Moreover, these two schemes provide the approximate solutions with first-order and second-order accuracy in time increment, respectively.