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DOI: 10.23952/jnfa.2026.10
Received October 10, 2025; Accepted December 20, 2025; Published April 1, 2026
Abstract. For the high-order finite element discretization system of three-dimensional elasticity problems, a local multigrid (LMG) method based on bisection grids is proposed. By decomposing the high-order finite element space into a “high-frequency” component and a linear element space, and leveraging the properties of bisection grids and interpolation operators, the stability of this space decomposition and the validity of the strong Cauchy-Schwarz inequality are proven. Consequently, the uniform convergence of the LMG algorithm is established. Numerical experiments are provided to verify the correctness of the theoretical results.
How to Cite this Article:
L. Zhou, Y. Lin, Convergence of local multigrid for high-order adaptive FEM in 3D elasticity problems, J. Nonlinear Funct. Anal. 2026 (2026) 10.