# Questions tagged [l2-norm]

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### Frobenius norm of a binary matrix

In term of the mathematical distance measurement, What is the significance of a Frobenius norm for a binary matrix?
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### About the discrete $H^1$ norm

I need to understand what is the right expression for the "discrete $H^1$-norm of a function v(which of course need to be in $H^1$). By definition, $$||v||_{H^1}^2 = ||\nabla v||_{2}^2 + ||v||_2^2$$ ...
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### Fastest way to calculate the $2$-norm (or an upper bound for the $2$-norm) of the inverse of a matrix $A\in \mathbb{C}^{N\times N}$

I have a matrix $A\in \mathbb{C}^{N\times N}$ and I need to calculate $||A^{-1}||_{2}$ efficiently. Can it be done without having to evaluate the inverse explicitly? In general, I am looking for ...
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### How I could calculate L2 norm of an unstructured grid?

I want to calculate L2 norm of a 3D unstructured grid to compare my simulation results in two different mesh sizes as coarse and fine. I read this answer and it seems in three-dimensional space, I ...
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### Estimate $L_2$ norm of a elliptic problem with unknown exact solution on finite element method

I have the elliptic problem $$-\Delta u = 1,\,\,\Omega\subset\mathbb{R}^2$$ with $u=0$ on $\partial\Omega,$ with $\Omega=[-1,1]^2\backslash([0,1]\times[-1,0])$ and I want to estimate the $L_2$ error ...
### $L^2$-error in FEM: how to compute integral over reference element?
I have the following problem. The domain is $(0,1)$ and we consider a uniform triangulation on $\hat{\Omega}$ with elements $K_i = [i/N,(i+1)/N]$ and $X_h^1$ the linear finite element space. I wrote ...
For the heat equation \begin{equation} u_t(t,x) = \nu u_{xx}(t,x) \end{equation} for $x \in [0,1]$ with boundary conditions $u(t,0) = u(t,1) = 0$ and initial value $u(0,x) = u_0(x)$ it is easy to ...