H~1-Galerkin Mixed Finite Element Methods For Semilinear Pseudo-Hyperbolic Partial Integro-Differential Equation

An H1-Galerkin mixed finite element method is discussed for a semilinear pseudo-hyperbolic partial integro-differential equation. The existence of its mixed generalized solution, semi-discrete and fully discrete mixed finite element solutions are discussed, and their error estimates are ana-lyzed, and it is showed that the H1-Galerkin mixed finite element method do not require the LBB consistency condition. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.