scholarly journals A cut-cell finite element method for Poisson’s equation on arbitrary planar domains

2021 ◽  
Vol 383 ◽  
pp. 113875
Author(s):  
Sushrut Pande ◽  
Panayiotis Papadopoulos ◽  
Ivo Babuška
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Planar Domains ◽  
Cut Cell ◽  
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.

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