An a posteriori error reduction scheme for the three-dimensional finite element solution of Maxwell's equations

1995 ◽  
Vol 43 (2) ◽  
pp. 421-427 ◽  
Author(s):  
U. Pekel ◽  
R. Lee
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Posteriori Error ◽  
Error Reduction ◽  
Element Solution ◽  
A Posteriori ◽  
Reduction Scheme ◽  
A Posteriori Error ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Effective Convergence Checks for Verifying Finite Element Stresses at Three-Dimensional Stress Concentrations

2018 ◽  
Vol 3 (3) ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair ◽  
P. J. Roache
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
A Posteriori Error Estimates ◽  
Three Dimensional ◽  
Posteriori Error ◽  
Test Problems ◽  
A Posteriori ◽  
Stress Concentrations ◽  
Element Analysis ◽  
A Posteriori Error

Current computational capabilities facilitate the application of finite element analysis (FEA) to three-dimensional geometries to determine peak stresses. The three-dimensional stress concentrations so quantified are useful in practice provided the discretization error attending their determination with finite elements has been sufficiently controlled. Here, we provide some convergence checks and companion a posteriori error estimates that can be used to verify such three-dimensional FEA, and thus enable engineers to control discretization errors. These checks are designed to promote conservative error estimation. They are applied to twelve three-dimensional test problems that have exact solutions for their peak stresses. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 111 error assessments for the test problems. For these 111, errors are assessed as being at the same level as true exact errors on 99 occasions, one level worse for the other 12. Hence, stress error estimation that is largely reasonably accurate (89%), and otherwise modestly conservative (11%).

Adaptive Refinement for 3-D Finite Element Analysis

1993 ◽  
Author(s):  
S. N. Muthukrishnan ◽  
R. V. Namblar ◽  
K. L. Lawrence
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Posteriori Error ◽  
Adaptive Refinement ◽  
A Posteriori ◽  
Element Analysis ◽  
A Posteriori Error ◽  
Simple Strategy ◽  
Element Size ◽  
Adaptive Nature

Abstract A simple strategy to adaptively refine three dimensional tetrahedral meshes has been implemented. A method of refinement for both plane faced and curve faced elements is presented in this paper. Examples are presented in which the rcmeshing is based on a refinement ratio determined from an a-posteriori error indicator obtained from the finite element solution of the problem. The resulting finite element meshes have a smooth gradient in element size. Example meshes are included to show the adaptive nature of the remesher when applied over several solution cycles.

Sign in / Sign up

Export Citation Format

Share Document