A remark on least-squares Galerkin procedures for pseudohyperbolic equations

In this paper, we introduce two split least-squares Galerkin finite element procedures for pseudohyperbolic equations arising in the modelling of nerve conduction process. By selecting the least-squares functional properly, the procedures can be split into two sub-procedures, one of which is for the primitive unknown variable and the other is for the flux. The convergence analysis shows that both the two methods yield the approximate solutions with optimal accuracy in L2(Ω)L2(Ω) norm for uu and utut and (L2(Ω))2(L2(Ω))2 norm for the flux σσ. Moreover, the two methods get approximate solutions with first-order and second-order accuracy in time increment, respectively. A numerical example is given to show the efficiency of the introduced schemes.