docstring - also use of exec is not recommended. please expand parameters into keyword args.

docsting

docstring

Add comment describing what this function does and what the parameters do

missing docstring here

perhaps indicate this explicitly in the figure

Quality of the approach: meets Quality of the writing: meets Quality of the figures/tables: meets

Is the code made publicly available and does the article sufficiently describe how to access it? yes

Does the article present the problem in an appropriate context? Specifically, does it:

• explain why the problem is important --> yes
• describe in which situations it arises --> yes
• outline relevant previous work -> some, cannot judge full extent
• provide background information for non-experts -> yes

Is the content of the paper accessible to a computational scientist with no specific knowledge in the given field?

the article does provide some background that made it easier for me to follow, but i do not have sufficient expertise in Galerkin discretization approaches, but the general idea of using multi resolution solvers to iteratively approximate the true solution was conveyed in the article.

Does the paper describe a well-formulated scientific or technical achievement?

yes

Are the technical and scientific decisions well-motivated and clearly explained? Are the code examples (if any) sound, clear, and well-written?

yes. the code examples can be improved with better Python standards as noted.

Is the paper factual correct? Is the language and grammar of sufficient quality? Are the conclusions justified?

yes

Is prior work properly and fully cited?

i cannot comment on this.

Should any part of the article be shortened or expanded? Please explain. In your view, is the paper fit for publication in the conference proceedings? Please suggest specific improvements and indicate whether you think the article needs a significant rewrite (rather than a minor revision).

yes

include URL here

how is accuracy evaluated? is it simply || Au^\hat - b ||_2?