Analysis of split weighted least-squares procedures for pseudo-hyperbolic equations

In this paper, we introduce two novel split weighted least-squares finite element procedures for pseudo-hyperbolic equations arising in the modelling of nerve conduction process. By selecting the weighted least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable. Optimal order error estimates are developed and the numerical example is given to show the efficiency of the introduced schemes.