Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions

2021 ◽  
Author(s):  
Wen‐ming He ◽  
Ren Zhao ◽  
Yong Cao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Elliptic Problems ◽  
Richardson Extrapolation ◽  
Element Method

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

A stabilized discontinuous finite element method for elliptic problems

2002 ◽  
Vol 10 (1-2) ◽  
pp. 83-104 ◽  
Author(s):  
Richard E. Ewing ◽  
Junping Wang ◽  
Yongjun Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elliptic Problems ◽  
Discontinuous Finite Element ◽  
Discontinuous Finite Element Method ◽  
Element Method

Physical statement of the problem for a numerical model of soil freezing and heaving taking into account heat and mass transfer

2021 ◽  
pp. 244-256
Author(s):  
Виктор Григорьевич Чеверев ◽  
Евгений Викторович Сафронов ◽  
Алексей Александрович Коротков ◽  
Александр Сергеевич Чернятин
Keyword(s):  
Finite Element Method ◽  
Mass Transfer ◽  
Finite Element ◽  
Numerical Model ◽  
Boundary Conditions ◽  
Heat And Mass Transfer ◽  
Soil Freezing ◽  
The Finite Element Method ◽  
Freezing Front ◽  
Element Method

Существуют два основных подхода решения задачи тепломассопереноса при численном моделировании промерзания грунтов: 1) решение методом конечных разностей с учетом граничных условий (границей, например, является фронт промерзания); 2) решение методом конечных элементов без учета границ модели. Оба подхода имеют существенные недостатки, что оставляет проблему решения задачи для численной модели промерзания грунтов острой и актуальной. В данной работе представлена физическая постановка промерзания, которая позволяет создать численную модель, базирующуюся на решении методом конечных элементов, но при этом отражающую ход фронта промерзания - то есть модель, в которой объединены оба подхода к решению задачи промерзания грунтов. Для подтверждения корректности модели был проделан ряд экспериментов по физическому моделированию промерзания модельного грунта и выполнен сравнительный анализ полученных экспериментальных данных и результатов расчетов на базе представленной численной модели с такими же граничными условиями, как в экспериментах. There are two basic approaches to solving the problem of heat and mass transfer in the numerical modeling of soil freezing: 1) using the finite difference method taking into account boundary conditions (the boundary, for example, is the freezing front); 2) using the finite element method without consideration of model boundaries. Both approaches have significant drawbacks, which leaves the issue of solving the problem for the numerical model of soil freezing acute and up-to-date. This article provides the physical setting of freezing that allows us to create a numerical model based on the solution by the finite element method, but at the same time reflecting the route of the freezing front, i.e. the model that combines both approaches to solving the problem of soil freezing. In order to confirm the correctness of the model, a number of experiments on physical modeling of model soil freezing have been performed, and a comparative analysis of the experimental data obtained and the calculation results based on the provided numerical model with the same boundary conditions as in the experiments was performed.

Higher order meshless schemes applied to the finite element method in elliptic problems

2019 ◽  
Vol 77 (3) ◽  
pp. 779-802
Author(s):  
Sławomir Milewski ◽  
Roman Putanowicz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elliptic Problems ◽  
Higher Order ◽  
The Finite Element Method ◽  
Element Method

scholarly journals A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients

2018 ◽  
Vol 76 (8) ◽  
pp. 1950-1965 ◽  
Author(s):  
Zhaonan Dong ◽  
Emmanuil H. Georgoulis ◽  
Jeremy Levesley ◽  
Fuat Usta
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elliptic Problems ◽  
Random Coefficients ◽  
Stochastic Collocation ◽  
Sparse Kernel ◽  
Element Method
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