This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Recent advances in hardware, software, and communication technologies are enabling the design and implementation of a whole range of different types of networks that are being deployed in various environments. One such network that has received a lot of interest in the last couple of years is the Vehicular Ad-Hoc Network (VANET). VANET has become an active area of research, standardization, and development because it has tremendous potential to improve vehicle and road safety, traffic efficiency, and convenience as well as comfort to both drivers and passengers. Recent research efforts have placed a strong emphasis on novel VANET design architectures and implementations. A lot of VANET research work have focused on specific areas including routing, broadcasting, Quality of Service (QoS), and security. We survey some of the recent research results in these areas. We present a review of wireless access standards for VANETs, and describe some of the recent VANET trials and deployments in the US, Japan, and the European Union. In addition, we also briefly present some of the simulators currently available to VANET researchers for VANET simulations and we assess their benefits and limitations. Finally, we outline some of the VANET research challenges that still need to be addressed to enable the ubiquitous deployment and widespead adoption of scalable, reliable, robust, and secure VANET architectures, protocols, technologies, and services.

Vehicular ad hoc networks (VANETS): status, results, and challenges

We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubble functions, and the pressure by piecewise linear functions. We show that this element satisfies the usual inf-sup condition and converges with first order for both velocities and pressure. Finally we relate this element to families of higer order elements and to the popular Taylor-Hood element.

A stable finite element for the stokes equations

Vesicle pools and Ca2+ microdomains: new tools for understanding their roles in neurotransmitter release.

https://www.southampton.ac.uk/~nwb/lectures/GoodPracticeCFD/Articles/Validation_SAND2002-0529.pdf

Verification and Validation in Computational Fluid Dynamics

In this paper we derive error estimates for a class of finite element approximation of the Stokes equation. These elements, popular among engineers, are conforming lagrangian both in velocity and pressure and therefore based on a mixed variational principle. The error estimates are established from a new Brezzi-type inequality for this kind of mixed formulation. The results are true in 2 or 3 dimensions.

Error estimates for finite element method solution of the Stokes problem in the primitive variables

A finite-element method for incompressible non-Newtonian flows

Many textiles do not noticeably stretch under their own weight. Unfortunately, for better performance many cloth solvers disregard this fact. We propose a method to obtain very low strain along the warp and weft direction using Constrained Lagrangian Mechanics and a novel fast projection method. The resulting algorithm acts as a velocity filter that easily integrates into existing simulation code.

/pdf/efficient-simulation-of-inextensible-cloth-5dxlrnduew.pdf

Efficient simulation of inextensible cloth

SUMMARY The frequently used reduced integration method for solving incompressible flow problems 'a la penalty' is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.

Michel Bercovier

Papers

Error estimates for finite element method solution of the Stokes problem in the primitive variables

A finite-element method for incompressible non-Newtonian flows

Efficient simulation of inextensible cloth

Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements

A finite element for the numerical solution of viscous incompressible flows