We present a high-order mesh r-adaptation strategy based on a linear elasticity formulation within a continuous Galerkin spectral element method (CG-SEM) framework. The approach enables solution-driven mesh redistribution while preserving high-order accuracy and mesh validity. The computational mesh is modeled as an elastic solid, and nodal positions are obtained by solving a linear elasticity problem. A spatially varying elasticity tensor derived from solution features concentrates nodes in regions of interest while smoothly redistributing them elsewhere. Mesh motion is incorporated within the CG-SEM framework using an Arbitrary Lagrangian-Eulerian (ALE) formulation. The resulting mesh velocity enters the convective operator, and the geometric mapping is updated by enforcing the discrete Geometric Conservation Law (DGCL). This ensures exact free-stream preservation and prevents spurious source terms, allowing conservation and high-order accuracy to be maintained on moving meshes. The methodology is implemented in the GPU-accelerated compressible flow solver sod2d using OpenACC. Since redistribution does not alter element connectivity, the method is well suited for GPU-accelerated high-order discretizations where remeshing would incur in efficiency and scalability penalties. The methodology is applied to compressible flow problems in the transonic and supersonic regimes, where the mesh is dynamically adapted to concentrate resolution across shock waves. The increased resolution reduces numerical dissipation and improves solution accuracy. Results show that elasticity-based r-adaptation can follow shock motion and deformation in unsteady simulations, concentrating nodes along the shock front while preserving mesh quality, and high throughput on GPU architectures.