H~1-Galerkin Mixed Finite Element Methods For Pseudo-Hyperbolic Equations With Space-Time Coefficient

In this thesis, two H1-Galerkin mixed finite element methods are studied for a class of second-order pseudo-hyperbolic partial equations with space-time coefficient. Optimal error estimates of the scalar unknown and its gradient for semidiscrete scheme are derived for problems in one space dimension, and the stability, existence and uniqueness. What's more, compared to standard mixed methods, the proposed methods have several attractive features. First, they are not subject to the LBB consistency condition:The finite element spaces Vh and Wh may be different polynomial degrees without requiring the finite element mesh to be quasi-uniform about the L2-and H1-error estimates...