Numerical solutions of Boussinesq equation using Galerkin finite element method

2020 ◽  
Author(s):  
Yusuf Ucar ◽  
Alaattin Esen ◽  
Berat Karaagac
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boussinesq Equation ◽  
Numerical Solutions ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Element Method

scholarly journals A GALERKIN FINITE ELEMENT METHOD TO SOLVE FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS

2013 ◽  
Vol 18 (2) ◽  
pp. 260-273 ◽  
Author(s):  
Alaattin Esen ◽  
Yusuf Ucar ◽  
Nuri Yagmurlu ◽  
Orkun Tasbozan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Galerkin Finite Element Method ◽  
Diffusion Wave ◽  
Galerkin Finite Element ◽  
Base Functions ◽  
Element Method

In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L 2 and L ∞ are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.

scholarly journals Numerical Solutions of Steady Tensorial Transport Equations Using Discontinuous Galerkin Method Implemented in FreeFem++

2016 ◽  
Vol 8 (1) ◽  
pp. 29-39
Author(s):  
K. M. Helal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Discontinuous Galerkin ◽  
Numerical Solutions ◽  
Transport Equations ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Discontinuous Galerkin Finite Element ◽  
Reaction Equations ◽  
Element Method

AbstractThe main purpose of this paper is to approximate the solution of the steady tensorial transport equations using discontinuous Galerkin finite element method implemented with the finite element solver FreeFem++. After introducing the formulations of the tensorial transport equations, the analysis of its componentwise equations, i.e., advection-reaction equations have been discussed. Discretizing the transport problem using discontinuous Galerkin finite element method, the iterative fixed-point method is used to obtain the solutions. We present the numerical simulations of two-dimensional benchmark problem and observe the instability of elasticity. All the simulations are done using the script developed in FreeFem++.

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