Finite element approximation of electrostatic potential in one dimensional multilayer structures with quantized electronic charge

Computing ◽  
1990 ◽  
Vol 45 (3) ◽  
pp. 251-264 ◽  
Author(s):  
Ph. Caussignac ◽  
B. Zimmermann ◽  
R. Ferro
Keyword(s):  
Finite Element ◽  
Electrostatic Potential ◽  
Finite Element Approximation ◽  
Multilayer Structures ◽  
Electronic Charge ◽  
Element Approximation ◽  
One Dimensional

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

A one-dimensional quasi-static contact problem in linear thermoelasticity

1993 ◽  
Vol 4 (2) ◽  
pp. 151-174 ◽  
Author(s):  
M. I. M. Copetti ◽  
C. M. Elliott
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Numerical Experiments ◽  
Finite Element Approximation ◽  
Unilateral Contact ◽  
Element Approximation ◽  
Time Step ◽  
One Dimensional ◽  
Static Contact ◽  
Linear Thermoelasticity

The existence, uniqueness and regularity of the solution to a one-dimensional linear thermoelastic problem with unilateral contact of the Signorini type are established. A finite element approximation is described, and an error bound is derived. It is shown that if the time step is O(h2), then the error in L2 in the temperature and in L∞ in the displacement is O(h). Some numerical experiments are presented.

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
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