Finite Element Approximation of Elliptic Problems with Dirac Measure Terms in Weighted Spaces: Applications to One- and Three-dimensional Coupled Problems

2012 ◽  
Vol 50 (1) ◽  
pp. 194-215 ◽  
Author(s):  
Carlo D'Angelo
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Elliptic Problems ◽  
Finite Element Approximation ◽  
Weighted Spaces ◽  
Dirac Measure ◽  
Element Approximation ◽  
Coupled Problems

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

Assessment of Hex-Dominant Mesh Efficacy for Nonlinear Finite Element Method Structural Analyses

2004 ◽  
Author(s):  
Nissan Shoykhet ◽  
Elena S. Di Martino ◽  
David A. Vorp ◽  
Kenji Shimada
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Tetrahedral Mesh ◽  
Element Approximation ◽  
Symmetric Model ◽  
Hexahedral Mesh ◽  
Structural Problems ◽  
L2 Norm

The objective of this study is to compare different types of meshes for the solution of static structural problems under large deformation conditions, using nonlinear materials. The three types of mesh used in this study are a structured hexahedral mesh, an unstructured tetrahedral mesh, and a hex-dominant mesh generated automatically by the bubble packing algorithm, [1]. The two geometries tested were a hypothetical, partially symmetric model of an Abdominal Aortic Aneurysm (AAA), and a three dimensional representation of an in vivo AAA reconstructed from CT scan images (Fig 1). In order to evaluate the accuracy of the finite element approximation the mean square (or L2) norm of the error was estimated.

Finite element approximation of some indefinite elliptic problems

CALCOLO ◽  
1988 ◽  
Vol 25 (4) ◽  
pp. 379-395 ◽  
Author(s):  
I. Capuzzo Dolcetta ◽  
S. Finzi Vita
Keyword(s):  
Finite Element ◽  
Elliptic Problems ◽  
Finite Element Approximation ◽  
Element Approximation

Finite Element Solution and Dispersion Analysis for the Transient Structural Acoustics Problem

1990 ◽  
Vol 43 (5S) ◽  
pp. S381-S388 ◽  
Author(s):  
N. N. Abboud ◽  
P. M. Pinsky
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Dispersion Analysis ◽  
Time Dependent ◽  
Element Approximation ◽  
Element Formulation ◽  
Structural Acoustics ◽  
Boundary Operators

In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. The variational statement of the governing equations is developed from a Hamiltonian approach that is modified for nonconservative systems. The dispersive properties of finite element semidiscretizations of the three dimensional wave equation are examined. This analysis throws light on the performance of the finite element approximation over the entire range of wavenumbers and the effects of the order of interpolation, mass lumping, and direction of wave propagation are considered.

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