scholarly journals Time-Adaptive Determination of Drug Efficacy in Mathematical Model of HIV Infection

2021 ◽  
Author(s):  
L. Beilina ◽  
M. Eriksson ◽  
I. Gainova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hiv Infection ◽  
Adaptive Mesh Refinement ◽  
A Posteriori Error Estimates ◽  
Drug Efficacy ◽  
Adaptive Finite Element Method ◽  
Optimization Approach ◽  
Element Method

AbstractThe paper considers a time-adaptive finite element method for determination of drug efficacy in a parameter identification problem (PIP) for a system of ordinary differential equations (ODE) that describes dynamics of the primary human immunodeficiency virus (HIV) infection with drug therapy. Tikhonov’s regularization method, optimization approach and finite element method to solve this problem are presented. A posteriori error estimates in the Tikhonov’s functional and reconstructed parameter are derived. Based on these estimates a time adaptive algorithm is formulated and numerically tested for different scenarios of noisy observations of virus population function. Numerical results show a significant improvement of reconstruction of drug efficacy parameter using the local time-adaptive mesh refinement method compared to the gradient method applied on a uniform time mesh.

scholarly journals An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data

2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Nikolay Koshev ◽  
Larisa Beilina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bounded Operator ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Fredholm Integral Equations ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
Element Method

AbstractWe propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally simulated and experimental backscattered data measured in microtomography.

PHASE-FIELD SIMULATIONS OF EUTECTIC SOLIDIFICATION USING AN ADAPTIVE FINITE ELEMENT METHOD

2006 ◽  
Vol 20 (07) ◽  
pp. 853-867
Author(s):  
DENIS DANILOV ◽  
BRITTA NESTLER
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Phase Field ◽  
Adaptive Mesh Refinement ◽  
Evolution Equations ◽  
Adaptive Finite Element Method ◽  
Implicit Time ◽  
Eutectic Solidification ◽  
Process Conditions ◽  
Element Method

A finite element method with a semi-implicit time update and an adaptive mesh refinement is used to numerically simulate characteristic growth morphologies in binary eutectic alloys for varying process conditions. The evolution equations are based on a recently developed phase-field model.1 Microstructure formations in typical temperature-composition regions of the eutectic phase diagram are computed showing single cellular primary phase growth, melting of eutectics, eutectic and off-eutectic solidification. We consider 2D and 3D lamellar two-phase growths, analyze the angle conditions at the eutectic triple junctions for different surface entropy data and discuss the occurrence of wetting along the solid-solid interface.

scholarly journals A posteriori error estimates for a multi-scale finite-element method

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Khallih Ahmed Blal ◽  
Brahim Allam ◽  
Zoubida Mghazli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
A Posteriori Error Estimates ◽  
Numerical Test ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
A Posteriori ◽  
Essential Information ◽  
Multi Scale ◽  
Element Method

AbstractWe are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an a posteriori analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.

Three Dimensional Dynamic Analyses on Stroller Wheel with Shock Absorber

2013 ◽  
Vol 387 ◽  
pp. 159-163
Author(s):  
Yi Chern Hsieh ◽  
Minh Hai Doan ◽  
Chen Tai Chang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
The Road ◽  
Dimensional Finite Element ◽  
On The Road ◽  
Three Dimensional Finite Element ◽  
Element Method

We present the analyses of dynamics behaviors on a stroller wheel by three dimensional finite element method. The vibration of the wheel system causes by two different type barriers on the road as an experiment design to mimic the real road conditions. In addition to experiment analysis, we use two different packages to numerically simulate the wheel system dynamics activities. Some of the simulation results have good agreement with the experimental data in this research. Other interesting data will be measured and analyzed by us for future study and we will investigate them by using adaptive finite element method for increasing the precision of the computation results.

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