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

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.

Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems

2015 ◽  
Vol 8 (4) ◽  
pp. 582-604
Author(s):  
Zhengqin Yu ◽  
Xiaoping Xie
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Stability Result ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Quadrilateral Finite Element ◽  
Hybrid Stress Finite Element ◽  
Hybrid Stress

AbstractThis paper proposes and analyzes semi-discrete and fully discrete hybrid stress finite element methods for elastodynamic problems. A hybrid stress quadrilateral finite element approximation is used in the space directions. A second-order center difference is adopted in the time direction for the fully discrete scheme. Error estimates of the two schemes, as well as a stability result for the fully discrete scheme, are derived. Numerical experiments are done to verify the theoretical results.

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