Operator splitting for numerical solution of the modified Burgers' equation using finite element method

2018 ◽  
Vol 35 (2) ◽  
pp. 478-492 ◽  
Author(s):  
Yusuf Uçar ◽  
Nuri M. Yağmurlu ◽  
İhsan Çelikkaya
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Burgers Equation ◽  
Operator Splitting ◽  
Modified Burgers Equation ◽  
Element Method

scholarly journals Two Different Methods for Numerical Solution of the Modified Burgers’ Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Ali Başhan ◽  
Turabi Geyikli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Nonlinear Term ◽  
Burgers Equation ◽  
Unconditionally Stable ◽  
Von Neumann ◽  
B Spline ◽  
Modified Burgers Equation

A numerical solution of the modified Burgers’ equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computingL2andL∞error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.

scholarly journals APPLICATION OF GALERKIN FINITE ELEMENT METHOD IN THE SOLUTION OF 3D DIFFUSION IN SOLIDS

2009 ◽  
Vol 8 (2) ◽  
pp. 79 ◽  
Author(s):  
E. C. Romão ◽  
M. D. De Campos ◽  
J. A. Martins ◽  
L. F. M. De Moura
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Heat Diffusion ◽  
Average Error ◽  
Galerkin Finite Element Method ◽  
Diffusion In Solids ◽  
Galerkin Finite Element ◽  
L2 Norm ◽  
Element Method

This paper presents the numerical solution by the Galerkin Finite Element Method, on the three-dimensional Laplace and Helmholtz equations, which represent the heat diffusion in solids. For the two applications proposed, the analytical solutions found in the literature review were used in comparison with the numerical solution. The results analysis was made based on the the L2 Norm (average error throughout the domain) and L¥ Norm (maximum error in the entire domain). The two application results, one of the Laplace equation and the Helmholtz equation, are presented and discussed in order to to test the efficiency of the method.

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