Least-squares Galerkin procedures for pseudohyperbolic equations

Two least-squares Galerkin finite element schemes are formulated to solve pseudohyperbolic equations. The advantage of this method is that it is not subject to the LBB condition. The convergence analysis shows that the methods both yield the approximate solutions with optimal accuracy in (L2(Ω))2×L2(Ω)(L2(Ω))2×L2(Ω). Moreover, the two methods get the approximate solutions with first-order and second-order accuracy in time increment, respectively. Numerical example shows that the two schemes are effective.