Inquiry on Methods for Error Estimation without Analytical Solutions

General
1

Dear FEniCSx Community Members,

I am currently using FEniCSx to solve a finite element problem and have obtained a series of numerical solutions. In the absence of exact analytical solutions, I am seeking effective methods to estimate the error of these numerical solutions.

I would like to know:

  1. Does FEniCSx support these error estimation methods?
  2. If supported, how can I implement these methods within FEniCSx?
  3. Are there any code examples or tutorials available that I could refer to?

Any advice on how to implement these error estimation methods in FEniCSx would be greatly appreciated. Thank you for your time and assistance!

Best regards

2

FEniCS is a general purpose tool, so you can do most things in it, as long as you have a method in mind.

Maybe consider the following theoretical works

or

or for FEniCS specific error estimators

or
https://fenicsproject.org/pub/course/lectures/2013-11-logg-fcc/lecture_11_error_control.pdf
or

This is in general not my field of expertise, so I hope others can give you more advice (@jackhale?:slight_smile: )