# Questions tagged [error-estimation]

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### Roundoff errors in FEM computations - generalized eigenvalues

This is a continuation of my previous question. I am trying to effectively compute a bound for the roundoff errors in some FEM computation (2d polygons, triangular meshes). Below I will write some of ...
185 views

### Implementation of Z^2 error estimator in Abaqus for adaptive mesh refinement

Currently, I am working on a remeshing routine for my simulations (Abaqus 6.14-1) using python scripts. The simulation deals with the Brinell indentation test and as the remeshing software I use Gmsh ...
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### Different sources of error in Finite Element computations

Consider the problem $-\Delta u = f$ in $\Omega$, with $u=0$ on $\partial \Omega$. Suppose that $\Omega$ is a polygon and that we approximate the solutions to the previous problem using Lagrange ...
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### Question about step in the proof of standard discrete trace inequality

I'm studying from Guermond lecture notes available at https://www.math.tamu.edu/~guermond/M661_FALL_2019/chap12.pdf (see Lemma 12.8( Discrete trace inequality).) Consider the simple case $p=r$, i.e. ...
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59 views

### Error in Monte Carlo integration

I am looking for a concise description to help me understand the error for Monte Carlo Integration using Uniform Sampling and Importance Sampling For Importance Sampling I have that the error is just ...
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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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### Correct relative error for Comparison of levelsets outside a constrained region

I am working on the estimation of tumor extent outside of the region which is visible in MRT/CT/DTI images. I want to compare two methods, which approximate the tumor density profile. Lets say the ...
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### The proper way to assess the error of Jacobi iteration (for 2D Poisson equation)?

Motivation: I'm using 2D regular grid (it's actually a quadtree but I can still treat it as a finite difference thing if I weight-average the solution over smaller scale cells for the purpose of ...
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### Error propagation through an FFT

If I take the Fourier transform of data $x \pm \sigma$, is there a standard approach to what the error in the outputs will be? Would the best way be a direct evaluation of the upper and lower bounds?
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### Is resampling more accurate than block average for statistical analysis of data?

I'm working in laboratories where molecular dynamics data are almost always analysed usign block average as stated in the famous Allen and Tildesley book. We divide the datas in blocks of size $M$ on ...
82 views