Linear hybrid unstructured meshes are elevated to high-order meshes using a mesh smoothing scheme. The linear meshes are first elevated to highorder by introducing new edge, face and internal nodes. Then the high-order elements are subdivided into a collection of linear sub-elements. Node perturbation vectors are computed for the new surface nodes. Employing a mesh smoothing/optimization method on the linear sub-elements curves the high-order mesh. The mesh smoothing method is an extension of an optimization-based node perturbation technique that uses a cost function to enforce desired element shapes. Details of the mesh elevation and smoothing process are described. Several three-dimensional examples are included that demonstrate the effectiveness of the method to produce high quality highorder meshes.Nomenclature [A] = Jacobian matrix for condition number C, C min = Cost function, minimum cost function WCN = Weighted condition number J = Magnitude of Jacobian matrix ! p n = Perturbation vector for node n ! s n = Sensitivity vector for node n [W] = Weight matrix for weighted condition number X, Y, Z = Cartesian physical coordinates Ω = Relaxation parameter

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