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What is difference beetwen this two method? Are these methods far from each other or are these methods complement each other? Could you take an example?

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    $\begingroup$ Would you mind giving a bit more context (either to the question, or your own level of knowledge)? As it currently stands, your question is a bit like asking "how similar are optimization and calculus?", in that one might use CG to solve a linear system coming from an FE discretisation, but you could easily be doing something else. $\endgroup$ – origimbo Jan 28 at 15:38
  • $\begingroup$ Yes, my question is rather what is the relation between these methods, Wolfang take a good answer for me. $\endgroup$ – Konrad Jan 28 at 18:07
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The methods are unrelated. The finite element method is a way to convert a partial differential equation into a finite dimensional problem ("discretization") so it can be solved on a computer. The Conjugate Gradient method is a method to solve linear systems such as those that arise from the finite element method.

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