Lagrange Family Finite Elements Question
I am working on a project using my own hand made cobbled together FEM code. I have been using Linear Isoparametric elements in 2D for this code. I have it all working and it gives satisfactory results to simple problems like the sod shock tube. I am working on the Noh problem and find that around the shock front I am getting oscillations. Which is to be expected. I have a been told if I move to higher order Lagrange polynomials that this may help reduce the oscillations. I have gone through and added in the higher order elements (not using serendipity elements).
Here is my question with higher order elements you have interior nodes. These nodes won't connect to any other nodes in the Global Matrix (I form this for simple problems just to check myself). What do I do with them?
If I include them in the global formulation I get oscillatory behavior (I am setting up a test case of a uniform grid with no gradients of any type) that is through out the problem. I think the issue has to do with the interior nodes and how they are treated in the global equations but I am not sure what I am supposed to do with them. Any help is appreciated.
I figured out my issue it had nothing to do with the internal nodes after all. However since I had views of the thread I figured I should complete it. The answer to internal nodes is? Do nothing treat them as regular nodes in your solution matrix. You can consolidate them however I decided not to.
Hope this may help someone else,
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