# Questions tagged [error-estimation]

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### Scientific standards for numerical errors

In my field of research the specification of experimental errors is commonly accepted and publications which fail to provide them are highly criticized. At the same time I often find that results of ...
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### Why do equi-spaced points behave badly?

Experiment description: In Lagrange interpolation, the exact equation is sampled at $N$ points (polynomial order $N - 1$) and it is interpolated at 101 points. Here $N$ is varied from 2 to 64. Each ...
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### What are differences between 'a priori' and 'posteriori' error estimate in numerical analysis?

I have learnt about Finite Element Method (also a little on other numerical methods) but I don't know what are exactly definition of these two errors and differences between them?
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Most numerical methods for quadrature treat the integrand as a black-box function. What if we have more information? In particular, what benefit, if any, can we derive from knowing the first few ...
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### What are the relative benefits of using Adams-Moulton over Adams-Bashforth algorithm?

I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised ...
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### Estimating hardware error probability

Say I run a supercomputer computation on 100k cores for 4 hours on http://www.nersc.gov/users/computational-systems/edison/configuration, exchanging about 4 PB of data over the network and performing ...
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### Finite elements $W^{1,\infty}$ error estimates

Are there finite element method setups that provide error estimates in the $W^{1,\infty}$ norm (i.e., bounds on $\|u'_h - u'\|_\infty$)? Which families of elements can be used for implementing them? (...
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### How can I derive the a priori error estimate for a symmetric bilinear form using lagrange finite elements?

Suppose that I'm solving the poisson equation by the finite element method by lagrange elements. I know that the error can be measured in a variety of ways, depending on which norm you choose. For a ...
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### a priori error analysis of cell-centered finite-volume methods

I'm using the cell-centered finite-volume method (for example Morton, Numerical solution of convection-diffusion problems, Chapman&Hall, 1996) to discretize the advection-diffusion equation and ...
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### Error on a integral quantity with noise

First of all sorry if this is the wrong place to ask this question, I went to a few stack sites and thought here it would be more suitable. My problem: I have a physical quantity $F$ that depends on ...
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### Dividing functions over a wide range-

I try to solve a system of coupled equations, where a very nasty division operation occurs. In fact, I need to compute a derivative of two exponential decaying functions. Let's illustrate this with ...
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### $L^2$-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 ...
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### Problem Condition and Algorithm Stability

Consider 2 mathematical problems: $$f_1(x) = a - x \\ f_2(x) = e^x -1$$ The condition number for a function is defined as follows: $$k(f) = \left| x \cdot \frac{f'}{f} \right|$$ Lets analyze ...
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### How can you calculate percent error in tensor approximations?

I have a matrix A which is an approximation to the known matrix B. Both matrices are square, 3x3 matrices and, in this case, are ...
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### Error bars for pair-correlation function

I have obtained some data from neutron diffraction for some material samples. The "rawest" form of the data is the structure function $S(Q)$. We can choose a variety of different Q-maxes when ...
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### finite difference methods and global error

I was going through my notes on different finite difference methods and came across something I don't quite understand. I have code that will calculate an approximate solution we can call this $U_{nm}$...
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