I am looking for some examples for my Finite Elements project (in one dimension). I have written code in MATLAB and would like to show a few examples of it working. I have one or two general examples but am looking for one that isn't a classical solution, i.e one that cannot be solved directly. Can anyone suggest some please?
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An elliptic equation with a jump in the coefficient $ a $, perhaps? For example $((1+H (x))u_x)_x=0$ with some boundary conditions on $[-1,1] $. Here H is a Heaviside step function. – Ian Mar 26 '15 at 11:48
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Fab, I will give that a try. Thank you! – Carla White Mar 26 '15 at 11:58
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This question is unintentionally about finite elements which I show in my answer: http://math.stackexchange.com/questions/1205760/has-anybody-ever-considered-full-derivative/1205833#1205833 – Mar 26 '15 at 12:20
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One common example is bridges made from steel struts that can be treated as 1D beam elements. So, just make up some simple arrangement of struts.
bubba
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I'm sorry I don't understand what beam elements are and how to tie the method to things like bridges. I'm a mathematics student, not engineering so my project has been mostly theoretical. The coding I have done thus far has just been for general equations as I haven't looked at practical applications. I will be moving onto that next year I believe. – Carla White Mar 26 '15 at 11:52
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If I remember correctly, a beam is a 1D element that resists extension and compression, but not twisting or torque. Think of the struts of a bridge. – bubba Mar 26 '15 at 12:20