scholarly journals Finite element approximation of the modified Boussinesq equations using a stabilized formulation

2008 ◽  
Vol 57 (9) ◽  
pp. 1249-1268 ◽  
Author(s):  
Ramon Codina ◽  
José M. González‐Ondina ◽  
Gabriel Díaz‐Hernández ◽  
Javier Principe
Keyword(s):  
Finite Element ◽  
Boussinesq Equations ◽  
Finite Element Approximation ◽  
Element Approximation

scholarly journals Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-21
Author(s):  
Jae-Hong Pyo
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Boussinesq Equations ◽  
Finite Element Approximation ◽  
Navier Stokes ◽  
Element Approximation ◽  
Uzawa Method ◽  
Element Space ◽  
Fully Discrete ◽  
Discrete Finite Element

The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow.

An Angular Finite Element Method for the Solution of the Even-Parity Equation

2009 ◽  
Author(s):  
R. Becker ◽  
R. Koch ◽  
M. F. Modest ◽  
H.-J. Bauer
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Basis Functions ◽  
New Method ◽  
Discrete Ordinates ◽  
Test Case ◽  
Element Approximation ◽  
Promising Alternative ◽  
Element Discretization ◽  
Spatial Coordinates

The present article introduces a new method to solve the radiative transfer equation (RTE). First, a finite element discretization of the solid angle dependence is derived, wherein the coefficients of the finite element approximation are functions of the spatial coordinates. The angular basis functions are defined according to finite element principles on subdivisions of the octahedron. In a second step, these spatially dependent coefficients are discretized by spatial finite elements. This approach is very attractive, since it provides a concise derivation for approximations of the angular dependence with an arbitrary number of angular nodes. In addition, the usage of high-order angular basis functions is straightforward. In the current paper the governing equations are first derived independently of the actual angular approximation. Then, the design principles for the angular mesh are discussed and the parameterization of the piecewise angular basis functions is derived. In the following, the method is applied to two-dimensional test cases which are commonly used for the validation of approximation methods of the RTE. The results reveal that the proposed method is a promising alternative to the well-established practices like the Discrete Ordinates Method (DOM) and provides highly accurate approximations. A test case known to exhibit the ray effect in the DOM verifies the ability of the new method to avoid ray effects.

Finite Element Approximation of the p-Laplacian

1993 ◽  
Vol 61 (204) ◽  
pp. 523 ◽  
Author(s):  
John W. Barrett ◽  
W. B. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation
Sign in / Sign up

Export Citation Format

Share Document