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.

scholarly journals Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

2020 ◽  
Vol 30 (05) ◽  
pp. 847-865
Author(s):  
Gabriel Barrenechea ◽  
Erik Burman ◽  
Johnny Guzmán
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Inviscid Flow ◽  
Element Approximation ◽  
Well Posedness ◽  
Hodge Laplacian ◽  
Conforming Finite Element ◽  
Velocity Approximation

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using [Formula: see text](div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the [Formula: see text]-norm of order [Formula: see text]. We also prove error estimates for the pressure error in the [Formula: see text]-norm.

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.

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