# Questions tagged [error-estimation]

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### Step size updating scheme adaptive embedded RK methods

If I have a RK method $y$ of order $p$ and a RK method $z$ of order $p-1$ I have read I can estimate the local error as $r_{n+1} = y_{n+1} - z_{n+1}$. First of all I don't see how this estimates the ...
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### Asymptotic error of forward Euler

I'm trying to understand the asymptotic error behaviour of forward Euler (finite difference method), as timesteps are decreased (refined), so I feel trust in the method of manufactured solutions (MMS)....
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### Calculate accuracy order/rate

I was doing error analysis of numerical scheme and I get $L_1$ error for each grid size with $N$ element. I was searching reference to compute accuracy order/rate from that error data but doesn't find ...
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### Log-transformation of decision variables in parameter estimation

I am trying to find the diffusion coefficient ($D$) and the partition coefficient ($KLP$) using experimental data of desorption of a pollutant from a film into a liquid. This process can be modelled, ...
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### Polynomial approximation spaces

I often see people using products of 1-D polynomials to do interpolation or projection of smooth multivariate functions over grids or cells because it is intuitive and simple to implement. What are ...
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### Error control and sequence acceleration at the same time

In a posteriori error control for solving ODEs, one typically computes two different approximate solutions, one of which being "more accurate" and one of which being "less accurate". If $y_q^{n+1}$ is ...
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### Numerical analysis: Chebyshev coefficient representation error

If $x_k$ are the Chebyshev nodes, that is for $n \in \mathbb{N}^*$, we have $x_k = \cos(\pi \frac{2k + 1}{n})$. Now suppose you have approximated values of $x_k$ and $x_{k'}$ for $k,k' \leq n$. In the ...
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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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### FEM problem: how to get a feeling for size of problem

The following problem is given: $$- \bigtriangleup u = f, \quad \partial_n u = g \quad \text{on } \Gamma_N, \quad u = 0 \quad \text{on } \Gamma_D$$ with $\Gamma_N$ or $\Gamma_D$ denoting the ...
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### Modulus (absolute) of a function, its quadrature, and relevance of zeros

Modulus of a (discretized) function, $|f_h(x)|$, where $h$ refers to the mesh spacing, would, in general, have zeros, and those zeros would not necessarily lie exactly at the mesh points. A naive <...
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### Mesh error quantification using error norm for a sharp logistic function [closed]

Consider the following logistic function in 1D for the domain $0$ to $1$. $$f(x) = \frac{1}{1 + \exp(-50(x-0.5))}$$ Let's say I resolve this on two meshes: first with 11 equispaced points (0.0, 0....
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### Propagation of error in fitting two sets of data to each other

I have two sets of experimental data: $\phi(t)$ and $I(t)$. In theory they are related to each other as: $\phi(t) = nI(t)$. By fitting these curves together I can find the value of $n$ (which is a ...
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### Error measure for a simple finite difference scheme

I am responsible for assisting with certain error measurements for an FE program. The idea is to set up some benchmark comparisons which we can use for future development of the program. To simplify ...
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### Round-off errors in ratio of Gaussian functions

I would like to understand how division of round-off errors can lead to large errors??? I am using a method to measure the frequency dependent dissipation in simulations performed by Discontinuous ...
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### What does optimal convergence rate mean? How to prove whether a numerical method, e.g. FEM, has an optimal convergence rate or not?

I searched online about the way optimal is defined mathematically,but without any information acquired? How to prove whether a numerical method, e.g. FEM, has an optimal convergence rate or not? ...
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### error estimator VS error indicator in the context of FEM error estimation

Is an error indicator an index for size measurement of something? And how is the relationship between the error estimator and error indicator? Is the error indicator just used for the (e.g. derivative)...
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### Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now). My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
108 views

### Precision not improving by decreasing step-size in nonlinear Schrödinger

I tried to simulate soliton propagation by solving the nonlinear Schrödinger equation using the split-step Fourier method. The following is an example of the Matlab code copied from a textbook. ...
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### How group similar data in a single classes and reduce the error

I have vehicles gps information in my real time traffic application. Averaging that information I know the speed of every road at any time. The problem is that is too much data to send back to the ...
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### Quick evaluation of floating point Absolute Error

I need to to find a quick and dirty way to estimate the absolute error introduced by a series of agebraic operations of IEEE single precision floating point numbers, a pessimistic result is ok. The ...
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### Dirichlet term in error estimations

I am working on a method based on moving least square approximation where shape functions do not satisfy Kroneker Delta property. So Dirichlet boundary condition should be enforced. I usually used ...
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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 ...
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### Relationship between global and local error?

In some cases I have seen that if the local error is: $Err = O (\Delta t^{p+1})$ where the global error is p. So if local error is 3, global will be 2. Does somebody know where it comes? For ...
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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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### matlab lsqcurvefit parameter estimation journey

The lsqcurvefit solution in matlab converges at different solutions depending upon the initial guess: Surface represents the error (SSE) between model and data at various combinations of parameters ...
### $L^2$-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 ...
I have a multi-variate, continuous function $f$ from $R^n$ to $R$, which I can query for its output for any input. I would like to create interpolation polynomial for it. In one-dimensional case ...