# Questions tagged [numerics]

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### About the condition $\ker(B_h) \subset \ker(B)$ in mixed finite elements formulation

I'm studying mixed finite elements. The problem is a classical saddle-point one: we seek for $(u,p)$ in $V \times Q$: $$A u + B^t p = f$$ $$Bu = g$$ where $A: V \rightarrow V', B:V \rightarrow Q'$ ...
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### How to prove the stability of the interpolation?

From the book (Vidar Thomee, Galerkin finite element methods for parabolic problems), there holds (see Lemma 13.3) \begin{align}\label{eq} \|\nabla I_h u\|_{L_{\infty}}\leq C\|\nabla u\|_{L_{\infty}},\...
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### How do you find the Jacobian matrix of a coordinate transformation given only dynamical data points?

Suppose you have a record of coordinates X(t) for every s units of time from 0 to time T. Suppose in addition you have more data Q(T) that is supposed to be output from some complex numerical ...
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### Perturbation problem using Runge-Kutta 4

I'm trying to evaluate the perturbations magnitude between 2 body orbiting a central one in three dimensions. In order to do this I need to have an estimate of the error, which I did using Richardson ...
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### Reference request: C++ and numerical analysis book

I'm a master student with a good Numerical analysis background. I'm going to do a master thesis in the same subject, but I need to use C++ since my advisor loves it, and I also believe it's the best ...