INTRODUCTION TO THE FINITE ELEMENT METHOD OTTOSEN PDF

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Articles about Massively Open Online Classes MOOCs had been rocking the academic world at least gently , and it seemed that your writer had scarcely experimented with teaching methods. Particularly compelling was the fact that there already had been some successes reported with computer programming classes in the online format, especially as MOOCs.

Finite Element Methods, with the centrality that computer programming has to the teaching of this topic, seemed an obvious candidate for experimentation in the online format. From there to the video lectures that you are about to view took nearly a year. I first had to take a detour through another subject, Continuum Physics, for which video lectures also are available, and whose recording in this format served as a trial run for the present series of lectures on Finite Element Methods.

Here they are then, about 50 hours of lectures covering the material I normally teach in an introductory graduate class at University of Michigan. The treatment is mathematical, which is natural for a topic whose roots lie deep in functional analysis and variational calculus. It is not formal, however, because the main goal of these lectures is to turn the viewer into a competent developer of finite element code.

We do spend time in rudimentary functional analysis, and variational calculus, but this is only to highlight the mathematical basis for the methods, which in turn explains why they work so well. Much of the success of the Finite Element Method as a computational framework lies in the rigor of its mathematical foundation, and this needs to be appreciated, even if only in the elementary manner presented here.

A background in PDEs and, more importantly, linear algebra, is assumed, although the viewer will find that we develop all the relevant ideas that are needed. The development itself focuses on the classical forms of partial differential equations PDEs : elliptic, parabolic and hyperbolic. At each stage, however, we make numerous connections to the physical phenomena represented by the PDEs. For clarity we begin with elliptic PDEs in one dimension linearized elasticity, steady state heat conduction and mass diffusion.

We then move on to three dimensional elliptic PDEs in scalar unknowns heat conduction and mass diffusion , before ending the treatment of elliptic PDEs with three dimensional problems in vector unknowns linearized elasticity. Parabolic PDEs in three dimensions come next unsteady heat conduction and mass diffusion , and the lectures end with hyperbolic PDEs in three dimensions linear elastodynamics.

Interspersed among the lectures are responses to questions that arose from a small group of graduate students and post-doctoral scholars who followed the lectures live. It is hoped that these lectures on Finite Element Methods will complement the series on Continuum Physics to provide a point of departure from which the seasoned researcher or advanced graduate student can embark on work in continuum computational physics.

Current research interests include: 1 mathematical and physical modelling of tumor growth, 2 cell mechanics 3 chemo-mechanically driven phenomena in materials, such as phase transformations and stress-influenced mass transport.

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Introduction to Finite Element Methods

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Introduction to the finite element method

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INTRODUCTION TO THE FINITE ELEMENT METHOD OTTOSEN PDF

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