A splitting positive definite mixed finite element method for two classes of integro-differential equations

Abstract

In this article, we establish a new mixed finite element procedure to solve the second-order hyperbolic and pseudo-hyperbolic integro-differential equations, in which the mixed element system is symmetric positive definite without requiring the LBB consistency condition. Convergence analysis shows that the method yields the approximate solutions with optimal accuracy in L2(Ω) norm for u and in H( div;Ω) norm for the flux σ. Numerical experiments are given to verify the theoretical results.