Involutive Completion to Avoid LBB Condition

2008 ◽  
pp. 497-504
Author(s):  
B. Mohammadi ◽  
J. Tuomela
Keyword(s):  
Lbb Condition

On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations

2016 ◽  
Vol 16 (3) ◽  
pp. 507-522 ◽  
Author(s):  
Yanhui Su ◽  
Lizhen Chen ◽  
Xianjuan Li ◽  
Chuanju Xu
Keyword(s):  
Lower Bound ◽  
Error Estimate ◽  
Spectral Method ◽  
Stokes Equations ◽  
Necessary Condition ◽  
Well Posedness ◽  
Saddle Point Problems ◽  
Numerical Examples ◽  
Lbb Condition ◽  
Optimal Lower Bound

AbstractThe Ladyženskaja–Babuška–Brezzi (LBB) condition is a necessary condition for the well-posedness of discrete saddle point problems stemming from discretizing the Stokes equations. In this paper, we prove the LBB condition and provide the (optimal) lower bound for this condition for the triangular spectral method proposed by L. Chen, J. Shen, and C. Xu in [3]. Then this lower bound is used to derive an error estimate for the pressure. Some numerical examples are provided to confirm the theoretical estimates.

A Stabilized Mixed FEM for Viscoplastic Flow Analysis

2000 ◽  
Author(s):  
Yong Liu ◽  
Antoinette M. Maniatty ◽  
Ottmar Klaas ◽  
Mark S. Shephard
Keyword(s):  
Mixed Finite Element ◽  
Flow Analysis ◽  
Mixed Finite Element Method ◽  
Viscoplastic Flow ◽  
Lagrange Equations ◽  
Flow Problems ◽  
Bulk Forming ◽  
Mixed Fem ◽  
Lbb Condition ◽  
Stabilized Mixed Finite Element

Abstract A stabilized, mixed finite element method for viscoplastic flow analysis is presented. Preliminary results show promise for modeling steady-state bulk forming processes. In this work, the Ladyzenskaya-Babuska-Brezzi (LBB) condition is circumvented by adding mesh dependent terms (stabilization terms), which are functions of the residual of the Euler-Lagrange equations, to the usual Galerkin method. The stabilized formulation and applications to plastic flow problems are presented. Numerical experiments using the stabilization method show that the stabilized, mixed FEM is effective and efficient for non-linear steady forming problems.

Role of the LBB Condition in Weak Spectral Projection Methods

2001 ◽  
Vol 174 (1) ◽  
pp. 405-420 ◽  
Author(s):  
F. Auteri ◽  
J.-L. Guermond ◽  
N. Parolini
Keyword(s):  
Spectral Projection ◽  
Projection Methods ◽  
Lbb Condition

Leak-Before-Break Assessment of a Cracked Reactor Vessel Nozzle Using 3D Crack Meshes

2016 ◽  
Author(s):  
Greg Thorwald ◽  
Lucie Parietti
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Surface Crack ◽  
Best Practice ◽  
Element Analysis ◽  
Reference Stress ◽  
Lbb Condition ◽  
Crack Stability ◽  
Leak Before Break

A postulated surface crack near a reactor pressure vessel nozzle is evaluated using finite element analysis (FEA) to compute the fatigue crack growth rate, evaluate crack stability, and examine the possibility of a leak-before-break (LBB) condition. For a pressurized vessel with cyclic loading, determining if the crack may have a LBB condition is desirable to allow for the possibility of leak detection leading to corrective action before catastrophic failure. A fatigue crack growth analysis is used to determine how the surface crack dimensions develop before re-categorizing the surface crack as a through thickness crack and evaluating its stability for LBB. To evaluate if a particular crack is unstable and may cause a structural failure, the Failure Assessment Diagram (FAD) method provides an evaluation using two ratios: brittle fracture and plastic collapse. The FAD method is described in the engineering best practice standard API 579-1/ASME FFS-1. The FAD curve and assessment ratios can be obtained from crack front J-integral values, which are computed using 3D crack meshes and elastic and elastic-plastic FEA. Computing custom crack solutions is beneficial when structural component geometries do not have an available stress intensity or reference stress solution.

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