Finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement

2020 ◽  
Vol 372 ◽  
pp. 113445
Author(s):  
Mirza Cenanovic ◽  
Peter Hansbo ◽  
Mats G. Larson
Keyword(s):  
Finite Element ◽  
Mean Curvature ◽  
Mesh Refinement ◽  
Triangulated Surfaces

Mesh Refinement Formulations in Adaptive Finite Element Methods

1996 ◽  
Vol 210 (4) ◽  
pp. 353-361 ◽  
Author(s):  
L-Y Li ◽  
P Bettess ◽  
J W Bull ◽  
T Bond
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Mesh Refinement ◽  
Adaptive Finite Element ◽  
Global Level ◽  
Adaptive Finite Element Methods ◽  
Element Level ◽  
Adaptive Remeshing ◽  
Numerical Examples ◽  
New Ideas

This paper presents some new ideas for developing adaptive remeshing strategies. It is shown that correct mesh refinement formulations should be defined at an element level rather than a global level. To accomplish this, permissible element errors are required to be defined. This paper describes the methods to determine the permissible element errors. Two mesh refinement formulations are derived according to different accuracy definitions and are compared with the conventional mesh refinement formulation derived at the global level. Numerical examples are shown to explain the features of these mesh refinement formulations. Recommendations are made for use of these mesh refinement formulations.

Adaptive finite element analysis of free vibration of elastic membranes via element energy projection technique

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Haohan Sun ◽  
Si Yuan
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Mesh Refinement ◽  
Error Tolerance ◽  
Maximum Norm ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Local Mesh Refinement ◽  
Elastic Membranes ◽  
Element Energy Projection

Purpose A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique. Design/methodology/approach By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems. Findings Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm. Originality/value By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.

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