scholarly journals A multilevel local mesh refinement with the PCD Method

2020 ◽  
Vol 39 (1) ◽  
pp. 213-225
Author(s):  
Ahmed Tahiri
Keyword(s):  
Diffusion Equation ◽  
Numerical Experiments ◽  
Mesh Refinement ◽  
Local Refinement ◽  
Computational Costs ◽  
Local Mesh Refinement

We propose in this contribution a successive local mesh refinement with the PCD method. The multilevel local refinement improves the accuracy and gives a better precision, locally and globally, with a lower computational costs particularly if the considered problem has an anomaly. Here we present how a successive local mesh refinement can be handled. We conclude by presenting numerical experiments to show the interest of a multilevel local mesh refinement for the 2D diffusion equation.

Local Mesh Refinement for Correlation of FEA Estimated Plastic Strain to Tests in Areas of High Plastic Strain

2018 ◽  
Author(s):  
Katharine Liu ◽  
Emma Xiao ◽  
Gregory Westwater ◽  
Christopher R. Johnson ◽  
J. Adin Mann
Keyword(s):  
Plastic Strain ◽  
Mesh Refinement ◽  
Sensitivity Study ◽  
Linear Elastic ◽  
Mesh Sensitivity ◽  
Local Mesh Refinement ◽  
Order Of Magnitude ◽  
High Plastic Strain ◽  
Stabilization Technique ◽  
The Impact

The total strain, elastic plus plastic, was measured with strain gages on valve bodies with internal pressure that caused surface yielding. The correlation of the simulated maximum principal strain was compared to strain gage data. A mesh sensitivity study shows that in regions of large plastic strain, mesh elements are required that are an order of magnitude smaller than what is used for linear elastic stress analysis for the same structure. A local mesh refinement was adequate to resolve the local high strain values. Both the location and magnitude of the maximum strain changed with a local mesh refinement. The local mesh refinement requirement was consistent over several structures that were tested. The test and simulation work will be presented along with the mesh sensitivity study. Some results on using an energy stabilization technique to aid convergence will be presented in terms of the impact on the predicted plastic strain.

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.

A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Ibrahim Karatay ◽  
Nurdane Kale ◽  
Serife Bayramoglu
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Caputo Derivative ◽  
Numerical Experiments ◽  
Time Derivative ◽  
Heat Equations ◽  
First Order ◽  
Fractional Heat Equation

AbstractIn this paper, we consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with the Caputo derivative of order α, where 0 < α < 1. The main purpose of this work is to extend the idea on the Crank-Nicholson method to the time-fractional heat equations. By the method of the Fourier analysis, we prove that the proposed method is stable and the numerical solution converges to the exact one with the order O(τ 2-α + h 2), conditionally. Numerical experiments are carried out to support the theoretical claims.

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