Xiao, Yingxiong; Zhang, Hongmei; Shu, Shi Algebraic multigrid method for higher-order finite element equations in three dimensional linear elasticity. (Chinese. English summary) Zbl 1230.74038 Chin. J. Comput. Mech. 27, No. 6, 995-1000, 1015 (2010). Summary: As for the finite element method, higher-order elements are often used in that they are superior and necessary under certain conditions over low-order ones, for example, they can overcome Poisson’s ratio locking. However, they have much higher computational complexity than linear elements. In this paper, we firstly introduce this method for elliptic problems to the solution of three dimensional elasticity problems discretized using higher-order elements and propose a two-level method by algebraic approaches. With the existing algebraic multigrid (L_AMG) method used as a solver on the first coarse level, an AMG method is then designed for high-order discretizations. The results of various numerical experiments show that the AMG method designed in this paper is more robust and efficient for the solution of higher-order finite element equations in three dimensional linear elasticity. Cited in 1 Document MSC: 74B20 Nonlinear elasticity 74S05 Finite element methods applied to problems in solid mechanics Keywords:algebraic multigrid; higher-order elements; 3D elasticity problems; tetrahedron partition PDFBibTeX XMLCite \textit{Y. Xiao} et al., Chin. J. Comput. Mech. 27, No. 6, 995--1000, 1015 (2010; Zbl 1230.74038)