scholarly journals Finite Element Method to Solve Poisson’s Equation Using Curved Quadratic Triangular Elements

2019 ◽  
Vol 577 ◽  
pp. 012165
Author(s):  
G Shylaja ◽  
B Venkatesh ◽  
V Kesavulu Naidu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Triangular Elements ◽  
Element Method

scholarly journals LOCALIZATION OF SOLUTION OF THE PROBLEM FOR POISSON’S EQUATION WITH THE USE OF B-SPLINE DISCRETE-CONTINUAL FINITE ELEMENT METHOD

2021 ◽  
Vol 17 (3) ◽  
pp. 157-172
Author(s):  
Marina Mozgaleva ◽  
Pavel Akimov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Basis Functions ◽  
Poisson’S Equation ◽  
Numerical Implementation ◽  
Poisson's Equation ◽  
B Spline ◽  
Element Method

Localization of solution of the problem for Poisson’s equation with the use of B-spline discrete-continual finiteelement method (specificversion of wavelet-based discrete-continual finiteelement method) is under consideration in the distinctive paper. The original operational continual and discrete-continual formulations of the problem are given, some actual aspects of construction of normalized basis functions of a B-spline are considered, the corresponding local constructions for an arbitrary discrete-continual finiteelement are described, some information about the numerical implementation and an example of analysis are presented.

scholarly journals NUMERICAL SOLUTION OF THE PROBLEM FOR POISSON’S EQUATION WITH THE USE OF DAUBECHIES WAVELET DISCRETE-CONTINUAL FINITE ELEMENT METHOD

2021 ◽  
Vol 17 (4) ◽  
pp. 123-133
Author(s):  
Marina Mozgaleva ◽  
Pavel Akimov ◽  
Mojtaba Aslami
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Finite Element Approximation ◽  
Poisson’S Equation ◽  
Element Approximation ◽  
Daubechies Wavelet ◽  
Numerical Implementation ◽  
Poisson's Equation ◽  
Element Method

Numerical solution of the problem for Poisson’s equation with the use of Daubechies wavelet discrete continual finite element method (specific version of wavelet-based discrete-continual finite element method) is under consideration in the distinctive paper. The operational initial continual and discrete-continual formulations of the problem are given, several aspects of finite element approximation are considered. Some information about the numerical implementation and an example of analysis are presented.

A Four-Noded Triangular (Tr4) Element for Solid Mechanics Problems with Curved Boundaries

2019 ◽  
Vol 17 (01) ◽  
pp. 1844003 ◽  
Author(s):  
Jun Hong Yue ◽  
Guirong Liu ◽  
Ruiping Niu ◽  
Ming Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solid Mechanics ◽  
Accurate Approximation ◽  
Shape Functions ◽  
Curved Boundaries ◽  
Triangular Elements ◽  
Complicated Geometry ◽  
Element Method ◽  
Physics Problems

Linear triangular elements with three nodes (Tr3) were the earliest, simplest and most widely used in finite element (FE) developed for solving mechanics and other physics problems. The most important advantages of the Tr3 elements are the simplicity, ease in generation, and excellent adaptation to any complicated geometry with straight boundaries. However, it cannot model well the geometries with curved boundaries, which is known as one of the major drawbacks. In this paper, a four-noded triangular (Tr4) element with one curved edge is first used to model the curved boundaries. Two types of shape functions of Tr4 elements have been presented, which can be applied to finite element method (FEM) models based on the isoparametric formulation. FE meshes can be created with mixed linear Tr3 and the proposed Tr4 (Tr3-4) elements, with Tr3 elements for interior and Tr4 elements for the curved boundaries. Compared to the pure FEM-Tr3, the FEM-Tr3-4 can significantly improve the accuracy of the solutions on the curved boundaries because of accurate approximation of the curved boundaries. Several solid mechanics problems are conducted, which validate the effectiveness of FEM models using mixed Tr3-4 meshes.

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