Analysis of mixed finite element methods for fourth-order wave equations

Mixed finite element methods, explicit and implicit in time, for a fourth-order wave equation are considered in this paper. The optimal error estimates in the L2L2 norm for velocity and moment and in the H1H1 norm and L2L2 norm for displacement are derived. These error estimates are proved by using a special interpolation operator on quasi-uniform rectangular meshes. The stabilities of the two schemes are also analyzed. In addition, three other kinds of mixed scheme are constructed. Numerical examples are provided to verify the theoretical results.