scholarly journals Superconvergent Flux Recovery of the Rannacher–Turek Nonconforming Element

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Yuwen Li
Keyword(s):  
Nonconforming Element

scholarly journals Application of P1-Nonconforming Element for Shell Structure of Incompressible Materiel

2011 ◽  
Vol 2-3 ◽  
pp. 1051-1056
Author(s):  
Lei Chen ◽  
Gang Won Jang ◽  
Tae Jin Chung ◽  
Tae Hyun Baek
Keyword(s):  
Topology Optimization ◽  
Shell Structure ◽  
Optimization Design ◽  
Incompressible Material ◽  
High Order ◽  
Solid Shell ◽  
Shell Elements ◽  
Volumetric Locking ◽  
Nonconforming Element ◽  
Nonconforming Elements

This research focused on solving volumetric locking problem of shell structure of incompressible material. Degenerated solid-shell elements are widely applied on curved structure. But, volumetric locking will take place when the structure is made of incompressible material, such as rubber. Due to Poisson’s locking free property of P1-nonconforming element, it is employed to solve volumetric locking problem of shell structure. Furthermore, the study on shell structure is extended to topology optimization design. To verify the volumetric locking free of P1-nonconforming element on shell structure of incompressible material, some structures are studied by different elements. Comparing with the utilization of high order elements to solve volumetric locking problems, P1-nonconforming elements can save calculation time and reduce the numerical cost.

A Two-Grid Method of Nonconforming Element Based on the Shifted-Inverse Power Method for the Steklov Eigenvalue Problem

2013 ◽  
Vol 694-697 ◽  
pp. 2918-2921
Author(s):  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
High Efficiency ◽  
Grid Method ◽  
Inverse Power ◽  
Power Method ◽  
Discretization Scheme ◽  
Nonconforming Element ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Numer Anal

This paper establishes a new kind of two-grid discretization scheme of nonconforming Crouzeix-Raviart element based on the shifted-inverse power method for the Steklov eigenvalue problem. The error estimates are provided from the work of Yang and Bi (SIAM J. Numer. Anal., 49, pp.1602-1624, 2011). Finally, numerical experiments are reported to illustrate the high efficiency of the two-grid discretization scheme proposed in this paper.

An Optimal Multilevel Method with One Smoothing Step for the Morley Element

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shibing Tang ◽  
Xuejun Xu
Keyword(s):  
Finite Element ◽  
Dirichlet Problem ◽  
Computational Complexity ◽  
Numerical Experiments ◽  
Multilevel Methods ◽  
Multilevel Method ◽  
Morley Element ◽  
Nonconforming Element ◽  
Linear Algebraic Systems ◽  
Multilevel Preconditioning

Abstract In this paper, a class of multilevel preconditioning schemes is presented for solving the linear algebraic systems resulting from the application of Morley nonconforming element approximations to the biharmonic Dirichlet problem. Based on an appropriate space splitting of the finite element spaces associated with the refinements and the abstract Schwarz framework, we prove that the proposed multilevel methods with one smoothing step are optimal, i.e., the convergence rate is independent of the mesh sizes and mesh levels. Moreover, the computational complexity is also optimal since the smoothers are performed only once on each level in the algorithm. Numerical experiments are provided to confirm the optimality of the suggested methods.

A nonconforming element for the Reissner–Mindlin plate

2003 ◽  
Vol 81 (8-11) ◽  
pp. 515-522 ◽  
Author(s):  
F. Brezzi ◽  
L.D. Marini
Keyword(s):  
Mindlin Plate ◽  
Nonconforming Element
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