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We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without algebraic constraints. Our error analysis, which is based on a new elliptic projection operator, applies to several mixed finite element spaces developed for elastostatics. The error estimates we obtain are robust for nearly incompressible materials.doi:10.1137/13095032x fatcat:k6uubvjwgrdiflnx5qogiii3qi