scholarly journals Constructive error analysis of a full-discrete finite element method for the heat equation

2019 ◽  
Vol 36 (3) ◽  
pp. 777-790 ◽  
Author(s):  
Kouji Hashimoto ◽  
Takuma Kimura ◽  
Teruya Minamoto ◽  
Mitsuhiro T. Nakao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Analysis ◽  
Heat Equation ◽  
Discrete Finite Element ◽  
Element Method

The Semi-Discrete Finite Element Method for the Cauchy Equation

2014 ◽  
Vol 668-669 ◽  
pp. 1130-1133
Author(s):  
Lei Hou ◽  
Xian Yan Sun ◽  
Lin Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Cauchy Equation ◽  
The Time Domain ◽  
Nicolson Scheme ◽  
Discrete Finite Element ◽  
Better Than ◽  
Element Method ◽  
Crank Nicolson

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

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