Abstract
We establish that the approximate solution of the mixed finite element method for the primary function is superconvergent to its $$L_2$$ local projection on unstructured meshes. To the best of our knowledge, all of the superconvergent results concerning mixed method need some conditions such as requiring the underlying meshes to be structured or using higher-order approximation spaces. Our results are valid on shape regular meshes, and any order of approximation spaces can be used. As an elementary consequence, we provide a proof that solutions of least-squares (LS) finite element method are higher-order perturbations of the solutions of the mixed and standard Galerkin methods. Also, we provide an $$L_2$$ norm error estimate for LS finite element solution on graded meshes.
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