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Nonlinear Continuum Mechanics for Finite Element Analysis by Javier Bonet and Richard D. Wood: Great book for getting a feel and good understanding of Continuum Mechanics.

The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T.J.R. Hughes: Great book for Finite Elements.  

Gilbert Strang is a great teacher. I am a big fan of his MIT OCW lectures. Do visit Gilbert Strang’s homepage.

A nice PDF on order parameters by James P. Sethna which is taken from his book Statistical Mechanics: Entropy, Order Parameters and Complexity

Legendre- Fenchel transforms in a nutshell by Hugo Touchette (PDF)

The Feynman Lectures on Physics is online.

1D FEM code with adaptive meshing in Matab: This code was written while I was in the first semester of my masters, and was specifically for the purpose of an assignment in a course offered by Antonio Orlando. It is far from optimised, but some might still find it useful as a starting point. Suggestions if any, are welcome. You may download the problem statement and MATLAB code.

The .zip file consists of the following matlab scripts
FEMad.m : Main driving script
elemstiff1D.m : Computation of stiffness matrix
elemload1D.m : Computation of load vector
estimator.m : Computing the vector of the estimates (explicit residual)
averaging.m : Averaging error estimator
insert.m : Inserts new element when re-meshing is required

Students of the COMMAS course C2 would have worked with a modified version of this code that two colleagues (Daniele Rosato and Dominic Zäh) and I prepared. We removed the adaptivity part and expanded the code to accommodate inelastic effects as well in order to teach students about different material models in the context of FEM programming.

Finite volume solver in C++ for steady-state groundwater flow equation (elliptic pde):
***To be uploaded soon!***

Salient features:
Compressed Row Storage (CRS) scheme for sparse matrices
Implementation of Successive Over Relaxation (SOR) and Conjugate Gradient (CG) methods
Parallelisation with OpenMP

 

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