Two Nonconforming Mixed Finite Element Method For Semilinear Pseudo-hyperbolic Partial Integro-differential Equations

In this paper, the nonconforming mixed finite element methods are studied for semi-linear pseudo-hyperbolic partial integro-differential equations. Depending on the physical quantities of interest, two numerical schemes are discussed.First, introducing the auxiliary variable p=-(a(?)ut+b(?)u+∫0t c(?)udτ), we formulate the weak formulation for mixed finite element method and semi-discrete nonconforming mixed element scheme. And we prove the existence and uniqueness of the solution of semi-discrete mixed scheme and the optimal error estimates for semi-discrete scheme.Second, we introduce the auxiliary variable p=aVu to formulate another semi-discrete mixed element scheme. And the existence and uniqueness of the solution and the optimal error estimates for semi-discrete scheme are derived.