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DOI: 10.23952/jnfa.2024.17
Received Apri 27, 2024; Accepted August 11, 2024; Published September 19, 2024
Abstract. The adaptive finite element method is an effective numerical approach for solving three-dimensional elasticity problems. This paper presents an adaptive p order finite element method which does not require marking oscillatory terms and does not satisfy the inner node property when refining meshes. Subsequently, aiming at the p order finite element equations under the adaptive meshes, a multigrid (MG) method based on local relaxation iteration is established by utilizing the characteristic that only local units on each layer of the meshes needs to be refined during the adaptive encryption process. Numerical experiments demonstrate that the adaptive finite element method exhibits uniform convergence and quasi-optimal computational complexity for linear and quadrtic finite element equations, and the corresponding multigrid method demonstrates good computational efficiency and robustness.
How to Cite this Article:
L. Zhou, H. Xu, Local multigrid method for solving adaptive finite element equations of three-dimensional elasticity problems, J. Nonlinear Funct. Anal. 2024 (2024) 17.